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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/06.01.23.0055.01









  


  








Input Form





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








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