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docs: update equations
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Planeshifter committed Jul 8, 2023
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Expand Up @@ -29,7 +29,7 @@ The [inverse coversed cosine][inverse-coversed-cosine] is defined as
<!-- <equation class="equation" label="eq:arccovercosine" align="center" raw="\operatorname{acovercos}(\theta) = \arcsin(1+\theta)" alt="Inverse coversed cosine."> -->

```math
\operatorname{acovercos}(\theta) = \arcsin(1+\theta)
\mathop{\mathrm{acovercos}}(\theta) = \arcsin(1+\theta)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{acovercos}(\theta) = \arcsin(1+\theta)" data-equation="eq:arccovercosine">
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Expand Up @@ -29,7 +29,7 @@ The [inverse coversed sine][inverse-coversed-sine] is defined as
<!-- <equation class="equation" label="eq:arccoversine" align="center" raw="\operatorname{acoversin}(\theta) = \arcsin(1-\theta)" alt="Inverse coversed sine."> -->

```math
\operatorname{acoversin}(\theta) = \arcsin(1-\theta)
\mathop{\mathrm{acoversin}}(\theta) = \arcsin(1-\theta)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{acoversin}(\theta) = \arcsin(1-\theta)" data-equation="eq:arccoversine">
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Expand Up @@ -29,7 +29,7 @@ The [inverse half-value versed cosine][archavercosine] is defined as
<!-- <equation class="equation" label="eq:archavercosine" align="center" raw="\operatorname{ahavercos}(\theta) = 2 \cdot \arccos(\sqrt{\theta})" alt="Inverse half-value versed cosine."> -->

```math
\operatorname{ahavercos}(\theta) = 2 \cdot \arccos(\sqrt{\theta})
\mathop{\mathrm{ahavercos}}(\theta) = 2 \cdot \arccos(\sqrt{\theta})
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{ahavercos}(\theta) = 2 \cdot \arccos(\sqrt{\theta})" data-equation="eq:archavercosine">
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Expand Up @@ -29,7 +29,7 @@ The [inverse half-value versed sine][archaversine] is defined as
<!-- <equation class="equation" label="eq:archaversine" align="center" raw="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" alt="Inverse half-value versed sine."> -->

```math
\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})
\mathop{\mathrm{ahaversin}}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" data-equation="eq:archaversine">
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Expand Up @@ -29,7 +29,7 @@ The [inverse versed cosine][inverse-versed-cosine] is defined as
<!-- <equation class="equation" label="eq:arcvercosine" align="center" raw="\operatorname{avercos}(\theta) = \arccos(1+\theta)" alt="Inverse versed cosine."> -->

```math
\operatorname{avercos}(\theta) = \arccos(1+\theta)
\mathop{\mathrm{avercos}}(\theta) = \arccos(1+\theta)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{avercos}(\theta) = \arccos(1+\theta)" data-equation="eq:arcvercosine">
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Expand Up @@ -29,7 +29,7 @@ The [inverse versed sine][inverse-versed-sine] is defined as
<!-- <equation class="equation" label="eq:arcversine" align="center" raw="\operatorname{aversin}(\theta) = \arccos(1-\theta)" alt="Inverse versed sine."> -->

```math
\operatorname{aversin}(\theta) = \arccos(1-\theta)
\mathop{\mathrm{aversin}}(\theta) = \arccos(1-\theta)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{aversin}(\theta) = \arccos(1-\theta)" data-equation="eq:arcversine">
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4 changes: 2 additions & 2 deletions lib/node_modules/@stdlib/math/base/special/beta/README.md
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Expand Up @@ -29,7 +29,7 @@ The [beta function][beta-function], also called the Euler integral, is defined a
<!-- <equation class="equation" label="eq:beta_function" align="center" raw="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" alt="Equation for the beta function."> -->

```math
\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t
\mathop{\mathrm{Beta}}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" data-equation="eq:beta_function">
Expand All @@ -44,7 +44,7 @@ The [beta function][beta-function] is related to the [Gamma function][gamma-func
<!-- <equation class="equation" label="eq:beta_function2" align="center" raw="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" alt="Beta function expressed in terms of the Gamma function."> -->

```math
\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!
\mathop{\mathrm{Beta}}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" data-equation="eq:beta_function2">
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4 changes: 2 additions & 2 deletions lib/node_modules/@stdlib/math/base/special/betaln/README.md
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Expand Up @@ -29,7 +29,7 @@ The [beta function][beta-function], also called the Euler integral, is defined a
<!-- <equation class="equation" label="eq:beta_function" align="center" raw="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" alt="Equation for the beta function."> -->

```math
\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t
\mathop{\mathrm{Beta}}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t" data-equation="eq:beta_function">
Expand All @@ -44,7 +44,7 @@ The [beta function][beta-function] is related to the [gamma function][gamma-func
<!-- <equation class="equation" label="eq:beta_function2" align="center" raw="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" alt="Beta function expressed in terms of the Gamma function."> -->

```math
\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!
\mathop{\mathrm{Beta}}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Beta}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!" data-equation="eq:beta_function2">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/ccis/README.md
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Expand Up @@ -29,7 +29,7 @@ The [cis][cis] function is defined as
<!-- <equation class="equation" label="eq:cis_function" align="center" raw="\operatorname{cis}(z) = e^{iz} = \cos(z) + i \sin(z)" alt="cis function"> -->

```math
\operatorname{cis}(z) = e^{iz} = \cos(z) + i \sin(z)
\mathop{\mathrm{cis}}(z) = e^{iz} = \cos(z) + i \sin(z)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{cis}(z) = e^{iz} = \cos(z) + i \sin(z)" data-equation="eq:cis_function">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/cexp/README.md
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Expand Up @@ -29,7 +29,7 @@ The [exponential][exponential-function] function of a complex number is defined
<!-- <equation class="equation" label="eq:cexp_function" align="center" raw="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" alt="Complex exponential function"> -->

```math
\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))
\mathop{\mathrm{exp}}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{exp}(z) = e^{x + i y} = (\exp{x}) (\cos(y) + i \sin(y))" data-equation="eq:cexp_function">
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Expand Up @@ -29,7 +29,7 @@ The [coversed cosine][coversed-cosine] is defined as
<!-- <equation class="equation" label="eq:covercosine" align="center" raw="\operatorname{covercos}(\theta) = 1 + \sin \theta" alt="Coversed cosine."> -->

```math
\operatorname{covercos}(\theta) = 1 + \sin \theta
\mathop{\mathrm{covercos}}(\theta) = 1 + \sin \theta
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{covercos}(\theta) = 1 + \sin \theta" data-equation="eq:covercosine">
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Expand Up @@ -29,7 +29,7 @@ The [coversed sine][coversed-sine] is defined as
<!-- <equation class="equation" label="eq:coversine" align="center" raw="\operatorname{coversin}(\theta) = 1 - \sin \theta" alt="Coversed sine."> -->

```math
\operatorname{coversin}(\theta) = 1 - \sin \theta
\mathop{\mathrm{coversin}}(\theta) = 1 - \sin \theta
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{coversin}(\theta) = 1 - \sin \theta" data-equation="eq:coversine">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/erf/README.md
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Expand Up @@ -29,7 +29,7 @@ The [error function][error-function] is defined as
<!-- <equation class="equation" label="eq:error_function" align="center" raw="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" alt="Error function."> -->

```math
\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt
\mathop{\mathrm{erf}}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,\mathrm dt" data-equation="eq:error_function">
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4 changes: 2 additions & 2 deletions lib/node_modules/@stdlib/math/base/special/erfc/README.md
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Expand Up @@ -29,7 +29,7 @@ The [complementary error function][complementary-error-function] is defined as
<!-- <equation class="equation" label="eq:complementary_error_function" align="center" raw="\operatorname{erfc}(x) = 1 - \operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt" alt="Complementary error function."> -->

```math
\operatorname{erfc}(x) = 1 - \operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt
\mathop{\mathrm{erfc}}(x) = 1 - \mathop{\mathrm{erf}}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erfc}(x) = 1 - \operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt" data-equation="eq:complementary_error_function">
Expand All @@ -44,7 +44,7 @@ The [complementary error function][complementary-error-function] can also be exp
<!-- <equation class="equation" label="eq:craigs_formula" align="center" raw="\operatorname{erfc}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta" alt="Craig's formula of the complementary error function."> -->

```math
\operatorname{erfc}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta
\mathop{\mathrm{erfc}}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erfc}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta" data-equation="eq:craigs_formula">
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Expand Up @@ -29,7 +29,7 @@ The [inverse complementary error function][erfcinv] is defined as
<!-- <equation class="equation" label="eq:inverse_complementary_error_function" align="center" raw="\operatorname{erfc}^{-1}(1-z) = \operatorname{erf}^{-1}(z)" alt="Inverse complementary error function."> -->

```math
\operatorname{erfc}^{-1}(1-z) = \operatorname{erf}^{-1}(z)
\mathop{\mathrm{erfc}}^{-1}(1-z) = \mathop{\mathrm{erf}}^{-1}(z)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erfc}^{-1}(1-z) = \operatorname{erf}^{-1}(z)" data-equation="eq:inverse_complementary_error_function">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/erfcx/README.md
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Expand Up @@ -29,7 +29,7 @@ The scaled [complementary error function][complementary-error-function] is defin
<!-- <equation class="equation" label="eq:scaled_complementary_error_function" align="center" raw="\operatorname{erfcx}(x) = e^{x^2} \operatorname{erfc}(x)" alt="Scaled complementary error function."> -->

```math
\operatorname{erfcx}(x) = e^{x^2} \operatorname{erfc}(x)
\mathop{\mathrm{erfcx}}(x) = e^{x^2} \mathop{\mathrm{erfc}}(x)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erfcx}(x) = e^{x^2} \operatorname{erfc}(x)" data-equation="eq:scaled_complementary_error_function">
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Expand Up @@ -29,7 +29,7 @@ The [inverse error function][inverse-error-function] is defined in terms of the
<!-- <equation class="equation" label="eq:inverse_error_function" align="center" raw="\operatorname{erf}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}" alt="Inverse error function."> -->

```math
\operatorname{erf}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}
\mathop{\mathrm{erf}}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{erf}^{-1}(z)=\sum_{k=0}^\infty\frac{c_k}{2k+1}\left (\frac{\sqrt{\pi}}{2}z\right )^{2k+1}" data-equation="eq:inverse_error_function">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/expit/README.md
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Expand Up @@ -29,7 +29,7 @@ The [standard logistic][logistic-function] function, also called the expit funct
<!-- <equation class="equation" label="eq:expit_function" align="center" raw="\begin{aligned}\operatorname{expit}(x) &= \frac{1}{1+e^{-x}} \\ &= \frac{e^{x}}{e^{x}+1} \\ &= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}" alt="Standard logistic function."> -->

```math
\begin{aligned}\operatorname{expit}(x) &= \frac{1}{1+e^{-x}} \\ &= \frac{e^{x}}{e^{x}+1} \\ &= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}
\begin{aligned}\mathop{\mathrm{expit}}(x) &= \frac{1}{1+e^{-x}} \\ &= \frac{e^{x}}{e^{x}+1} \\ &= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}
```

<!-- <div class="equation" align="center" data-raw-text="\begin{aligned}\operatorname{expit}(x) &amp;= \frac{1}{1+e^{-x}} \\ &amp;= \frac{e^{x}}{e^{x}+1} \\ &amp;= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}" data-equation="eq:expit_function">
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Expand Up @@ -29,7 +29,7 @@ The sign of the [gamma-function][@stdlib/math/base/special/gamma] is defined as
<!-- <equation class="equation" label="eq:gamma_sign_function" align="center" raw="\operatorname{gammasgn} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}" alt="Sign of the gamma function"> -->

```math
\operatorname{gammasgn} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}
\mathop{\mathrm{gammasgn}} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{gammasgn} ( x ) = \begin{cases} 1 &amp; \textrm{if}\ \Gamma &gt; 1 \\ -1 &amp; \textrm{if}\ \Gamma &lt; 1 \\ 0 &amp; \textrm{otherwise}\ \end{cases}" data-equation="eq:gamma_sign_function">
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Expand Up @@ -29,7 +29,7 @@ The half-value [coversed cosine][coversed-cosine] is defined as
<!-- <equation class="equation" label="eq:hacovercosine" align="center" raw="\operatorname{hacovercos}(\theta) = \frac{1 + \sin \theta}{2}" alt="Half-value coversed cosine."> -->

```math
\operatorname{hacovercos}(\theta) = \frac{1 + \sin \theta}{2}
\mathop{\mathrm{hacovercos}}(\theta) = \frac{1 + \sin \theta}{2}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{hacovercos}(\theta) = \frac{1 + \sin \theta}{2}" data-equation="eq:hacovercosine">
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Expand Up @@ -29,7 +29,7 @@ The half-value [coversed sine][coversed-sine] is defined as
<!-- <equation class="equation" label="eq:hacoversine" align="center" raw="\operatorname{hacoversin}(\theta) = \frac{1 - \sin \theta}{2}" alt="Half-value coversed sine."> -->

```math
\operatorname{hacoversin}(\theta) = \frac{1 - \sin \theta}{2}
\mathop{\mathrm{hacoversin}}(\theta) = \frac{1 - \sin \theta}{2}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{hacoversin}(\theta) = \frac{1 - \sin \theta}{2}" data-equation="eq:hacoversine">
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Expand Up @@ -29,7 +29,7 @@ The half-value [versed cosine][versed-cosine] is defined as
<!-- <equation class="equation" label="eq:havercosine" align="center" raw="\operatorname{havercos}(\theta) = \frac{1 + \cos \theta}{2}" alt="Haversed cosine."> -->

```math
\operatorname{havercos}(\theta) = \frac{1 + \cos \theta}{2}
\mathop{\mathrm{havercos}}(\theta) = \frac{1 + \cos \theta}{2}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{havercos}(\theta) = \frac{1 + \cos \theta}{2}" data-equation="eq:havercosine">
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Expand Up @@ -29,7 +29,7 @@ The half-value [versed sine][versed-sine] is defined as
<!-- <equation class="equation" label="eq:haversine" align="center" raw="\operatorname{haversin}(\theta) = \frac{1 - \cos \theta}{2}" alt="Haversed sine."> -->

```math
\operatorname{haversin}(\theta) = \frac{1 - \cos \theta}{2}
\mathop{\mathrm{haversin}}(\theta) = \frac{1 - \cos \theta}{2}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{haversin}(\theta) = \frac{1 - \cos \theta}{2}" data-equation="eq:haversine">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/logit/README.md
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Expand Up @@ -29,7 +29,7 @@ The [logit][logit] function is defined as the logarithm of the odds `p / (1-p)`;
<!-- <equation class="equation" label="eq:logit_function" align="center" raw="\operatorname{logit}(p)=\log \left({\frac {p}{1-p}}\right)" alt="Logit function."> -->

```math
\operatorname{logit}(p)=\log \left({\frac {p}{1-p}}\right)
\mathop{\mathrm{logit}}(p)=\log \left({\frac {p}{1-p}}\right)
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{logit}(p)=\log \left({\frac {p}{1-p}}\right)" data-equation="eq:logit_function">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/ramp/README.md
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Expand Up @@ -44,7 +44,7 @@ or, alternatively, in terms of the `max` function
<!-- <equation class="equation" label="eq:ramp_function_alternative_defn" align="center" raw="R(x) = \operatorname{max}( x, 0 )" alt="Ramp function alternative definition."> -->

```math
R(x) = \operatorname{max}( x, 0 )
R(x) = \mathop{\mathrm{max}}( x, 0 )
```

<!-- <div class="equation" align="center" data-raw-text="R(x) = \operatorname{max}( x, 0 )" data-equation="eq:ramp_function_alternative_defn">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/rampf/README.md
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Expand Up @@ -44,7 +44,7 @@ or, alternatively, in terms of the `max` function
<!-- <equation class="equation" label="eq:ramp_function_alternative_defn" align="center" raw="R(x) = \operatorname{max}( x, 0 )" alt="Ramp function alternative definition."> -->

```math
R(x) = \operatorname{max}( x, 0 )
R(x) = \mathop{\mathrm{max}}( x, 0 )
```

<!-- <div class="equation" align="center" data-raw-text="R(x) = \operatorname{max}( x, 0 )" data-equation="eq:ramp_function_alternative_defn">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/rcbrt/README.md
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Expand Up @@ -29,7 +29,7 @@ The reciprocal of the principal [cube root][cube-root] is defined as
<!-- <equation class="equation" label="eq:reciprocal_cube_root" align="center" raw="\operatorname{rcbrt}(x)=\frac{1}{\sqrt[3]{x}}" alt="Reciprocal cube root"> -->

```math
\operatorname{rcbrt}(x)=\frac{1}{\sqrt[3]{x}}
\mathop{\mathrm{rcbrt}}(x)=\frac{1}{\sqrt[3]{x}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{rcbrt}(x)=\frac{1}{\sqrt[3]{x}}" data-equation="eq:reciprocal_cube_root">
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2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/math/base/special/rsqrt/README.md
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Expand Up @@ -29,7 +29,7 @@ The reciprocal of the principal [square root][square-root] is defined as
<!-- <equation class="equation" label="eq:reciprocal_square_root" align="center" raw="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->

```math
\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}
\mathop{\mathrm{rsqrt}}(x)=\frac{1}{\sqrt{x}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
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Expand Up @@ -29,7 +29,7 @@ The reciprocal of the principal [square root][square-root] is defined as
<!-- <equation class="equation" label="eq:reciprocal_square_root" align="center" raw="\operatorname{rsqrtf}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->

```math
\operatorname{rsqrtf}(x)=\frac{1}{\sqrt{x}}
\mathop{\mathrm{rsqrtf}}(x)=\frac{1}{\sqrt{x}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{rsqrtf}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
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Expand Up @@ -29,7 +29,7 @@ The [signum][signum] function is defined as
<!-- <equation class="equation" label="eq:signum_function" align="center" raw="\operatorname{sign}(x) := \begin{cases} -1 & \textrm{if}\ x < 0 \\ 0 & \textrm{if}\ x = 0 \\ 1 & \textrm{if}\ x > 0 \end{cases}" alt="Signum function"> -->

```math
\operatorname{sign}(x) := \begin{cases} -1 & \textrm{if}\ x < 0 \\ 0 & \textrm{if}\ x = 0 \\ 1 & \textrm{if}\ x > 0 \end{cases}
\mathop{\mathrm{sign}}(x) := \begin{cases} -1 & \textrm{if}\ x < 0 \\ 0 & \textrm{if}\ x = 0 \\ 1 & \textrm{if}\ x > 0 \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{sign}(x) := \begin{cases} -1 &amp; \textrm{if}\ x &lt; 0 \\ 0 &amp; \textrm{if}\ x = 0 \\ 1 &amp; \textrm{if}\ x &gt; 0 \end{cases}" data-equation="eq:signum_function">
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