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 HypergeometricPFQRegularized

 http://functions.wolfram.com/07.32.03.0059.01

 Input Form

 HypergeometricPFQRegularized[{1, a, a, Subscript[a, 4], \[Ellipsis], Subscript[a, q + 1]}, {a + 1, a + 1, Subscript[a, 4] + 1, \[Ellipsis], Subscript[a, q + 1] + 1}, -1] == (1/(2 Gamma[a]^2 Product[Gamma[Subscript[a, j]], {j, 4, q + 1}])) (Sum[Product[If[l == k, 1, (PolyGamma[(Subscript[a, k] + 1)/2] - PolyGamma[Subscript[a, k]/2])/((Subscript[a, l] - Subscript[a, k]) (a - Subscript[a, k])^2)], {l, 4, q + 1}] + ((PolyGamma[(a + 1)/2] - PolyGamma[a/2])/(a - Subscript[a, k])) Product[1/(Subscript[a, l] - a), {l, 4, q + 1}], {k, 4, q + 1}] - (1/2) (PolyGamma[1, (a + 1)/2] - PolyGamma[1, a/2]) Product[1/(Subscript[a, l] - a), {l, 4, q + 1}]) /; Subscript[a, l] != Subscript[a, k] && 4 <= l <= q + 1 && 4 <= k <= q + 1 && l != k

 Standard Form

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 MathML Form

 q + 1 F ~ q ( 1 , a , a , a 4 , , a q + 1 ; a + 1 , a + 1 , a 4 + 1 , , a q + 1 + 1 ; - 1 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", RowBox[List[TagBox[SubscriptBox["a", RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "4"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "1"]], HypergeometricPFQ, Rule[Editable, True]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] 1 2 Γ ( a ) 2 j = 4 q + 1 Γ ( a j ) ( k = 4 q + 1 ( ψ TagBox["\[Psi]", PolyGamma] ( a + 1 2 ) - ψ TagBox["\[Psi]", PolyGamma] ( a 2 ) a - a k l = 4 q + 1 1 a l - a + l = 4 l k q + 1 ψ TagBox["\[Psi]", PolyGamma] ( a k + 1 2 ) - ψ TagBox["\[Psi]", PolyGamma] ( a k 2 ) ( a l - a k ) ( a - a k ) 2 ) - 1 2 ( ψ TagBox["\[Psi]", PolyGamma] ( 1 ) ( a + 1 2 ) - ψ TagBox["\[Psi]", PolyGamma] ( 1 ) ( a 2 ) ) l = 4 q + 1 1 a l - a ) /; a l a k 4 l q + 1 4 k q + 1 l k FormBox RowBox RowBox TagBox TagBox RowBox RowBox SubscriptBox FormBox RowBox q + 1 TraditionalForm SubscriptBox OverscriptBox F ~ FormBox q TraditionalForm RowBox ( RowBox TagBox 1 HypergeometricPFQ Rule Editable , TagBox a HypergeometricPFQ Rule Editable , TagBox a HypergeometricPFQ Rule Editable , TagBox SubscriptBox a 4 HypergeometricPFQ Rule Editable , TagBox HypergeometricPFQ Rule Editable , RowBox TagBox SubscriptBox a RowBox q + 1 HypergeometricPFQ Rule Editable ; TagBox TagBox RowBox TagBox RowBox a + 1 HypergeometricPFQ Rule Editable , TagBox RowBox a + 1 HypergeometricPFQ Rule Editable , TagBox RowBox SubscriptBox a 4 + 1 HypergeometricPFQ Rule Editable , TagBox HypergeometricPFQ Rule Editable , TagBox RowBox SubscriptBox a RowBox q + 1 + 1 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox RowBox - 1 HypergeometricPFQ Rule Editable ) InterpretTemplate Function HypergeometricPFQ Slot 1 Slot 2 Slot 3 Rule Editable HypergeometricPFQ RowBox FractionBox 1 RowBox 2 SuperscriptBox RowBox Γ ( a ) 2 RowBox UnderoverscriptBox RowBox j = 4 RowBox q + 1 RowBox Γ ( SubscriptBox a j ) RowBox ( RowBox RowBox UnderoverscriptBox RowBox k = 4 RowBox q + 1 ErrorBox RowBox ( RowBox RowBox FractionBox RowBox RowBox TagBox ψ PolyGamma ( FractionBox RowBox a + 1 2 ) - RowBox TagBox ψ PolyGamma ( FractionBox a 2 ) RowBox a - SubscriptBox a k RowBox UnderoverscriptBox RowBox l = 4 RowBox q + 1 FractionBox 1 RowBox SubscriptBox a l - a + RowBox UnderoverscriptBox UnderscriptBox RowBox l = 4 RowBox l k RowBox q + 1 FractionBox RowBox RowBox TagBox ψ PolyGamma ( FractionBox RowBox SubscriptBox a k + 1 2 ) - RowBox TagBox ψ PolyGamma ( FractionBox SubscriptBox a k 2 ) RowBox RowBox ( RowBox SubscriptBox a l - SubscriptBox a k ) SuperscriptBox RowBox ( RowBox a - SubscriptBox a k ) 2 ) - RowBox FractionBox 1 2 RowBox ( RowBox RowBox SuperscriptBox TagBox ψ PolyGamma RowBox ( 1 ) ( FractionBox RowBox a + 1 2 ) - RowBox SuperscriptBox TagBox ψ PolyGamma RowBox ( 1 ) ( FractionBox a 2 ) ) RowBox UnderoverscriptBox RowBox l = 4 RowBox q + 1 FractionBox 1 RowBox SubscriptBox a l - a ) /; RowBox RowBox SubscriptBox a l SubscriptBox a k RowBox 4 l RowBox q + 1 RowBox 4 k RowBox q + 1 RowBox l k TraditionalForm [/itex]

 Rule Form

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

 2001-10-29