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Mathematica Notation

Traditional Notation

Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Integration > Indefinite integration > Involving only one direct function with respect to a > For Phi^(z,s,a)




Input Form

Integrate[a^(\[Alpha] - 1) LerchPhiClassical[z, s, a], a] == (a^\[Alpha]/(\[Alpha] - s)) Sum[(z^k/((a + k)^s/((a + k)/a)^s)) Hypergeometric2F1[s - \[Alpha], s, 1 + s - \[Alpha], -(k/a)], {k, 0, Infinity}]

Standard Form

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MathML Form

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</ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> a </ci> <ci> &#945; </ci> </apply> <apply> <power /> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <ci> s </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; 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Rule Form

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