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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Summation > Infinite summation





http://functions.wolfram.com/01.02.23.0040.01









  


  








Input Form





Sum[1/((k + a)^n (k + b)^m), {k, 1, Infinity}] == ((-1)^(m + n)/((-a + b)^n (-1 + m)!)) Sum[(Binomial[-1 + m, k] Pochhammer[1 - k - n, k] PolyGamma[-1 - k + m, 1 + b])/(-a + b)^k, {k, 0, -1 + m}] - ((-1)^(m + n)/((-a + b)^m ((-1 + m)! (-1 + n)!))) Sum[(Binomial[-1 + n, k] k! Pochhammer[1 - k - m, -1 + m] PolyGamma[-1 - k + n, 1 + a])/(-a + b)^k, {k, 0, -1 + n}] /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0








Standard Form





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MathML Form







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Rule Form





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





2007-05-02