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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/06.01.23.0053.01









  


  








Input Form





Sum[(4 k)!/(4 k + 4 n)!, {k, 0, Infinity}] == (1/2) (Sum[-(2^j/((-2 + 4 n - j) (4 n - 1)!)), {j, 0, 4 n - 3}] + (2^(4 n) Log[2])/(4 (4 n - 1)!)) + (1/2) (Sum[-(((-1)^j 2^(-1 + 2 j) (10 + 20 n^2 + j (29 + 20 j) - n (29 + 40 j)))/((1 - n + j) (1 - 2 n + 2 j) (3 - 4 n + 4 j) (4 n - 1)!)), {j, 0, n - 2}] - ((3 2^(-1 + 2 n) (-1)^n) ((5 - Pi)/12 - Log[4]/12))/(4 n - 1)!) /; 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