html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 EllipticPi

 http://functions.wolfram.com/08.06.06.0101.01

 Input Form

 EllipticPi[n, z, m] == (-1)^Round[Re[z]/Pi] (Sqrt[Sin[z]^2]/Sqrt[(-m) Sin[z]^2]) ((-(1/(4 m Sin[z]^2))) Sum[(Pochhammer[3/2, k]/(m^k (k + 1)!)) HypergeometricPFQ[{1, 1, 3/2 + k}, {2 + k, 2}, 1/(m Sin[z]^2)] (n^k/Sqrt[1 - 1/n] - (Pochhammer[3/2, k]/(2 n (k + 1)!)) Hypergeometric2F1[1, 3/2 + k, 2 + k, 1/n]), {k, 0, Infinity}] + Sum[(Pochhammer[3/2, k]/(m^k (2 (1 + 2 k) k!))) (Log[(-m) Sin[z]^2] - PolyGamma[1/2 + k] + PolyGamma[1 + k]) (n^k/Sqrt[1 - 1/n] - (Pochhammer[3/2, k]/(2 n (k + 1)!)) Hypergeometric2F1[1, 3/2 + k, 2 + k, 1/n]), {k, 0, Infinity}] - ((3 Sin[z]^2)/(8 n)) Sum[((Pochhammer[5/2, i] Pochhammer[1/2, i])/(m^i (i! (2 + i)!))) Sum[(Sin[z]^(2 k) Pochhammer[1, k]^2 Pochhammer[1, j] Pochhammer[5/2 + i, j + k])/n^j/(j! k! Pochhammer[2, k] Pochhammer[3 + i, j + k]), {k, 0, Infinity}, {j, 0, Infinity}], {i, 0, Infinity}] + (Log[1 - n Sin[z]^2]/2) (1 - 1/Sqrt[1 - 1/n]) Sum[(Pochhammer[1/2, k] n^k)/(m^k k!), {k, 0, Infinity}] - Log[1 - n Sin[z]^2]/(2 Sqrt[1 - n/m])) + 2 Round[Re[z]/Pi] EllipticPi[n, m]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], FractionBox[SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]], SqrtBox[RowBox[List[RowBox[List["-", "m"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " "]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["3", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "k"]], ",", "2"]], "}"]], ",", FractionBox["1", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], "]"]], RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["n", "k"], SqrtBox[RowBox[List["1", "-", FractionBox["1", "n"]]]]], "-", RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], RowBox[List["2", " ", "n", RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", RowBox[List[FractionBox["3", "2"], "+", "k"]], ",", RowBox[List["2", "+", "k"]], ",", FractionBox["1", "n"]]], "]"]]]]]], ")"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " "]], RowBox[List["2", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], " ", RowBox[List["k", "!"]]]]], RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "m"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List[FractionBox["1", "2"], "+", "k"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "k"]], "]"]]]], ")"]], RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["n", "k"], SqrtBox[RowBox[List["1", "-", FractionBox["1", "n"]]]]], "-", RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], RowBox[List["2", " ", "n", RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", RowBox[List[FractionBox["3", "2"], "+", "k"]], ",", RowBox[List["2", "+", "k"]], ",", FractionBox["1", "n"]]], "]"]]]]]], ")"]]]]]], "-", RowBox[List[FractionBox[RowBox[List["3", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], RowBox[List["8", "n"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[" ", RowBox[List[SuperscriptBox["m", RowBox[List["-", "i"]]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "i"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "i"]], "]"]]]]]], RowBox[List[RowBox[List["i", "!"]], RowBox[List[RowBox[List["(", RowBox[List["2", "+", "i"]], ")"]], "!"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["n", RowBox[List["-", "j"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], RowBox[List["2", " ", "k"]]], " ", SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List["1", ",", "k"]], "]"]], "2"], " ", RowBox[List["Pochhammer", "[", RowBox[List["1", ",", "j"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["5", "2"], "+", "i"]], ",", RowBox[List["j", "+", "k"]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["j", "!"]], RowBox[List["k", "!"]], RowBox[List["Pochhammer", "[", RowBox[List["2", ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["3", "+", "i"]], ",", RowBox[List["j", "+", "k"]]]], "]"]]]], ")"]]]]]]]]]]]]]], " ", "+", RowBox[List[FractionBox[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["n", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]], "]"]], "2"], RowBox[List["(", RowBox[List["1", "-", FractionBox["1", SqrtBox[RowBox[List["1", "-", FractionBox["1", "n"]]]]]]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[" ", RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], SuperscriptBox["n", "k"], " "]]]], RowBox[List["k", "!"]]]]]]], " ", "-", FractionBox[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["n", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]], "]"]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", FractionBox["n", "m"]]]]]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]]]]]]]]

 MathML Form

 Π ( n ; z m ) ( - 1 ) Re ( z ) π sin ( z ) - m sin 2 ( z ) ( log ( 1 - n sin 2 ( z ) ) 2 ( 1 - 1 1 - 1 n ) k = 0 m - k ( 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] n k k ! - 1 4 m sin 2 ( z ) k = 0 m - k ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] ( k + 1 ) ! 3 F 2 ( 1 , 1 , k + 3 2 ; k + 2 , 2 ; 1 m sin 2 ( z ) ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", RowBox[List["m", " ", RowBox[List[SuperscriptBox["sin", "2"], "(", "z", ")"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ( n k 1 - 1 n - ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] 2 n ( k + 1 ) ! 2 F 1 ( 1 , k + 3 2 ; k + 2 ; 1 n ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["3", "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["k", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[FractionBox["1", "n"], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ) + k = 0 m - k ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] ( log ( - m sin 2 ( z ) ) + ψ TagBox["\[Psi]", PolyGamma] ( k + 1 ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 1 2 ) ) 2 ( 2 k + 1 ) k ! ( n k 1 - 1 n - ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] 2 n ( k + 1 ) ! 2 F 1 ( 1 , k + 3 2 ; k + 2 ; 1 n ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["3", "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["k", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[FractionBox["1", "n"], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ) - 3 sin 2 ( z ) 8 n i = 0 m - i ( 5 2 ) i TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "2"], ")"]], "i"], Pochhammer] ( 1 2 ) i TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "i"], Pochhammer] i ! ( i + 2 ) ! k = 0 j = 0 n - j sin 2 k ( z ) ( 1 ) k TagBox[SubscriptBox[RowBox[List["(", "1", ")"]], "k"], Pochhammer] 2 ( 1 ) j TagBox[SubscriptBox[RowBox[List["(", "1", ")"]], "j"], Pochhammer] ( i + 5 2 ) j + k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["i", "+", FractionBox["5", "2"]]], ")"]], RowBox[List["j", "+", "k"]]], Pochhammer] j ! k ! ( 2 ) k TagBox[SubscriptBox[RowBox[List["(", "2", ")"]], "k"], Pochhammer] ( i + 3 ) j + k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["i", "+", "3"]], ")"]], RowBox[List["j", "+", "k"]]], Pochhammer] - log ( 1 - n sin 2 ( z ) ) 2 1 - n m ) + 2 Re ( z ) π Π ( n m ) FormBox RowBox RowBox Π ( RowBox n ; RowBox z m ) RowBox RowBox SuperscriptBox RowBox ( RowBox - 1 ) ErrorBox RowBox FractionBox RowBox Re ( z ) π FractionBox RowBox sin ( z ) SqrtBox RowBox RowBox - m RowBox SuperscriptBox sin 2 ( z ) RowBox ( RowBox RowBox FractionBox RowBox log ( RowBox 1 - RowBox n RowBox SuperscriptBox sin 2 ( z ) ) 2 RowBox ( RowBox 1 - FractionBox 1 SqrtBox RowBox 1 - FractionBox 1 n ) RowBox UnderoverscriptBox RowBox k = 0 FractionBox RowBox SuperscriptBox m RowBox - k TagBox SubscriptBox RowBox ( FractionBox 1 2 ) k Pochhammer SuperscriptBox n k RowBox k ! - RowBox FractionBox 1 RowBox 4 m RowBox SuperscriptBox sin 2 ( z ) RowBox UnderoverscriptBox RowBox k = 0 RowBox FractionBox RowBox SuperscriptBox m RowBox - k TagBox SubscriptBox RowBox ( FractionBox 3 2 ) k Pochhammer RowBox RowBox ( RowBox k + 1 ) ! TagBox TagBox RowBox RowBox SubscriptBox 3 SubscriptBox F 2 RowBox ( RowBox TagBox TagBox RowBox TagBox 1 HypergeometricPFQ Rule Editable , TagBox 1 HypergeometricPFQ Rule Editable , TagBox RowBox k + FractionBox 3 2 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox TagBox RowBox TagBox RowBox k + 2 HypergeometricPFQ Rule Editable , TagBox 2 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox FractionBox 1 RowBox m RowBox SuperscriptBox sin 2 ( z ) HypergeometricPFQ Rule Editable ) InterpretTemplate Function HypergeometricPFQ Slot 1 Slot 2 Slot 3 Rule Editable HypergeometricPFQ RowBox ( RowBox FractionBox SuperscriptBox n k SqrtBox RowBox 1 - FractionBox 1 n - RowBox FractionBox TagBox SubscriptBox RowBox ( FractionBox 3 2 ) k Pochhammer RowBox 2 n RowBox RowBox ( RowBox k + 1 ) ! TagBox TagBox RowBox RowBox SubscriptBox 2 SubscriptBox F 1 RowBox ( RowBox TagBox TagBox RowBox TagBox 1 Hypergeometric2F1 Rule Editable , TagBox RowBox k + FractionBox 3 2 Hypergeometric2F1 Rule Editable InterpretTemplate Function SlotSequence 1 Hypergeometric2F1 Rule Editable ; TagBox TagBox TagBox RowBox k + 2 Hypergeometric2F1 Rule Editable InterpretTemplate Function SlotSequence 1 Hypergeometric2F1 Rule Editable ; TagBox FractionBox 1 n Hypergeometric2F1 Rule Editable ) InterpretTemplate Function HypergeometricPFQ Slot 1 Slot 2 Slot 3 Rule Editable Hypergeometric2F1 ) + RowBox UnderoverscriptBox RowBox k = 0 RowBox FractionBox RowBox SuperscriptBox m RowBox - k TagBox SubscriptBox RowBox ( FractionBox 3 2 ) k Pochhammer RowBox ( RowBox RowBox log ( RowBox RowBox - m RowBox SuperscriptBox sin 2 ( z ) ) + RowBox TagBox ψ PolyGamma ( RowBox k + 1 ) - RowBox TagBox ψ PolyGamma ( RowBox k + FractionBox 1 2 ) ) RowBox 2 RowBox ( RowBox RowBox 2 k + 1 ) RowBox k ! RowBox ( RowBox FractionBox SuperscriptBox n k SqrtBox RowBox 1 - FractionBox 1 n - RowBox FractionBox TagBox SubscriptBox RowBox ( FractionBox 3 2 ) k Pochhammer RowBox 2 n RowBox RowBox ( RowBox k + 1 ) ! TagBox TagBox RowBox RowBox SubscriptBox 2 SubscriptBox F 1 RowBox ( RowBox TagBox TagBox RowBox TagBox 1 Hypergeometric2F1 Rule Editable , TagBox RowBox k + FractionBox 3 2 Hypergeometric2F1 Rule Editable InterpretTemplate Function SlotSequence 1 Hypergeometric2F1 Rule Editable ; TagBox TagBox TagBox RowBox k + 2 Hypergeometric2F1 Rule Editable InterpretTemplate Function SlotSequence 1 Hypergeometric2F1 Rule Editable ; TagBox FractionBox 1 n Hypergeometric2F1 Rule Editable ) InterpretTemplate Function HypergeometricPFQ Slot 1 Slot 2 Slot 3 Rule Editable Hypergeometric2F1 ) - RowBox FractionBox RowBox 3 RowBox SuperscriptBox sin 2 ( z ) RowBox 8 n RowBox UnderoverscriptBox RowBox i = 0 RowBox FractionBox RowBox SuperscriptBox m RowBox - i TagBox SubscriptBox RowBox ( FractionBox 5 2 ) i Pochhammer TagBox SubscriptBox RowBox ( FractionBox 1 2 ) i Pochhammer RowBox RowBox i ! RowBox RowBox ( RowBox i + 2 ) ! RowBox UnderoverscriptBox RowBox k = 0 RowBox UnderoverscriptBox RowBox j = 0 FractionBox RowBox SuperscriptBox n RowBox - j RowBox SuperscriptBox sin RowBox 2 k ( z ) SuperscriptBox TagBox SubscriptBox RowBox ( 1 ) k Pochhammer 2 TagBox SubscriptBox RowBox ( 1 ) j Pochhammer TagBox SubscriptBox RowBox ( RowBox i + FractionBox 5 2 ) RowBox j + k Pochhammer RowBox RowBox j ! RowBox k ! TagBox SubscriptBox RowBox ( 2 ) k Pochhammer TagBox SubscriptBox RowBox ( RowBox i + 3 ) RowBox j + k Pochhammer - FractionBox RowBox log ( RowBox 1 - RowBox n RowBox SuperscriptBox sin 2 ( z ) ) RowBox 2 SqrtBox RowBox 1 - FractionBox n m ) + RowBox 2 RowBox FractionBox RowBox Re ( z ) π RowBox Π ( RowBox n m ) TraditionalForm [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["3", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "k"]], ",", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02