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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Summation > Finite summation > Various sums





http://functions.wolfram.com/01.02.23.0025.01









  


  








Input Form





Sum[z^k/((k + a)^2)^(s/2) - z^k/(k + a)^s, {k, 0, Floor[-Re[a]]}] == UnitStep[Floor[-Re[a]]] ((1 - E^((-(2 UnitStep[Im[a]] - 1)) Pi I s)) (LerchPhi[z, s, a] - z^Floor[-Re[a]]/((Floor[-Re[a]] + a)^2)^(s/2)) + (1 - UnitStep[Im[a]] (1 + Floor[-Re[a]] + Floor[Re[a]])) (((1 - E^((-(2 UnitStep[Im[a]] - 1)) Pi I s)) z^Floor[-Re[a]])/ ((Floor[-Re[a]] + a)^2)^(s/2)) - (1 - E^((-(2 UnitStep[Im[a]] - 1)) Pi I s)) z^(Floor[-Re[a]] + 1) LerchPhi[z, s, a + Floor[-Re[a]] + 1])








Standard Form





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MathML Form







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<ci> a </ci> </apply> </apply> <apply> <plus /> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> <apply> <floor /> <apply> <real /> <ci> a </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> s </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02