rule Sum(i_^k_*c_^(a_.*i_),{i_Symbol,1,Infinity}):=PolyLog(-k, c^a)

- https://www.johndcook.com/blog/2024/08/03/polylog/
axkr · Aug 4, 2024 · 0fe5ac9 · 0fe5ac9
1 parent 6ebb06f
commit 0fe5ac9
Show file tree

Hide file tree

Showing 3 changed files with 7 additions and 5 deletions.
diff --git a/...heclipse-core/src/main/java/org/matheclipse/core/reflection/system/rulesets/SumRules.java b/...heclipse-core/src/main/java/org/matheclipse/core/reflection/system/rulesets/SumRules.java
@@ -26,9 +26,9 @@ public static Matcher init1() {
     // Sum(k_^(a_.*i_),{i_Symbol,1,Infinity}):=-k^a/(-1+k^a)/;FreeQ(k,i)&&a<0&&(k>1||k<-1)
 matcher.caseOf(Sum(Power(k_,Times(a_DEFAULT,i_)),list(i_Symbol,C1,oo)),
       Condition(Times(CN1,Power(k,a),Power(Plus(CN1,Power(k,a)),CN1)),And(FreeQ(k,i),Less(a,C0),Or(Greater(k,C1),Less(k,CN1)))));
-    // Sum(i_^k_/c_^i_,{i_Symbol,1,Infinity}):=PolyLog(-k,1/c)/;FreeQ({c,k},i)
-matcher.caseOf(Sum(Times(Power(i_,k_),Power(c_,Negate(i_))),list(i_Symbol,C1,oo)),
-      Condition(PolyLog(Negate(k),Power(c,CN1)),FreeQ(list(c,k),i)));
+    // Sum(i_^k_*c_^(a_.*i_),{i_Symbol,1,Infinity}):=PolyLog(-k,c^a)/;FreeQ({a,c,k},i)
+matcher.caseOf(Sum(Times(Power(i_,k_),Power(c_,Times(a_DEFAULT,i_))),list(i_Symbol,C1,oo)),
+      Condition(PolyLog(Negate(k),Power(c,a)),FreeQ(list(a,c,k),i)));
     // Sum(x_^(2*i_+1)/(2*i_+1)!,{i_Symbol,0,Infinity}):=Sinh(x)/;FreeQ(x,i)
 matcher.caseOf(Sum(Times(Power(Factorial(Plus(Times(C2,i_),C1)),CN1),Power(x_,Plus(Times(C2,i_),C1))),list(i_Symbol,C0,oo)),
       Condition(Sinh(x),FreeQ(x,i)));

diff --git a/...a_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/SumTest.java b/...a_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/SumTest.java
@@ -446,6 +446,8 @@ public void testSumPolyLogInifinity() {
         "26");
     check("Sum(n^k/c^n,{n, 1, Infinity})", //
         "PolyLog(-k,1/c)");
+    check("Sum(n^k*c^(a*n),{n, 1, Infinity})", //
+        "PolyLog(-k,c^a)");
   }
 
   @Test

diff --git a/symja_android_library/rule_sets/SumRules.m b/symja_android_library/rule_sets/SumRules.m
@@ -13,8 +13,8 @@
 
 Sum(k_^(a_.*i_), {i_Symbol,1,Infinity}) := -(k^a)/(-1+(k^a))
   /; FreeQ(k,i) && a<0 && (k>1 || k<(-1)),
-Sum(i_^k_*c_^(-i_), {i_Symbol,1,Infinity}) := PolyLog(-k, 1/c)
-  /;  FreeQ({c,k},i), 
+Sum(i_^k_*c_^(a_.*i_), {i_Symbol,1,Infinity}) := PolyLog(-k, c^a)
+  /;  FreeQ({a,c,k},i), 
 
 Sum(x_^(2*i_+1)/(2*i_+1)!, {i_Symbol,0,Infinity}) := Sinh(x)
   /;  FreeQ(x,i),