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variants of this functions
Factorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Factorial[n] > Summation > Infinite summation > Parameter-containing sums





http://functions.wolfram.com/06.01.23.0025.01









  


  








Input Form





Sum[((-1)^k (2 k)!)/(2 k + 4 n + 1)!, {k, 0, Infinity}] == -Sum[((-1)^j 2^(1 + 2 j) (4 + 20 n^2 + j (19 + 20 j) - n (19 + 40 j)))/ ((1 - 2 n + 2 j) (1 - 4 n + 4 j) (3 - 4 n + 4 j) (4 n)!), {j, 0, n - 1}] + ((4^(n - 1) (-1)^n) Pi)/(4 n)! /; Element[n, Integers] && n > 0








Standard Form





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MathML Form







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Rule Form





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Contributed by





Troy Kessler


Date Added to functions.wolfram.com (modification date)





2007-05-02