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http://functions.wolfram.com/10.06.06.0039.01
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LerchPhiClassical[z, s, a] ==
Sum[(1/k!) Derivative[0, 0, k][LerchPhiClassical][z, s, Subscript[a, 0]]
(a - Subscript[a, 0])^k, {k, 0, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox["1", RowBox[List["k", "!"]]], RowBox[List[SuperscriptBox["LerchPhiClassical", TagBox[RowBox[List["(", RowBox[List["0", ",", "0", ",", "k"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z", ",", "s", ",", SubscriptBox["a", "0"]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", SubscriptBox["a", "0"]]], ")"]], "k"]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mi> s </mi> <annotation encoding='Mathematica'> TagBox["s", Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mi> a </mi> <annotation encoding='Mathematica'> TagBox["a", Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <mrow> <mrow> <msup> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", RowBox[List["0", ",", "0", ",", "k"]], ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <msub> <mi> a </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <msub> <mi> a </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> s </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> a </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <ci> k </ci> </list> <apply> <ci> OverHat </ci> <ci> Φ </ci> </apply> </apply> <ci> z </ci> <ci> s </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["LerchPhiClassical", TagBox[RowBox[List["(", RowBox[List["0", ",", "0", ",", "k"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z", ",", "s", ",", SubscriptBox["aa", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", SubscriptBox["aa", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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