Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ad1p)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, a₃>=3

For fixed z and a₁=-5/2, a₂=3, a₃=3

For fixed z and a₁=-5/2, a₂=3, a₃=3, b₁=-3/2

http://functions.wolfram.com/07.27.03.ad1p.01

Input Form

HypergeometricPFQ[{-(5/2), 3, 3}, {-(3/2), 3/2}, -z] == (1/(4096 (1 + z)^3)) (3616 - 21032 z + 233388 z^2 + 99225 Pi^2 z^(5/2) + 968436 z^3 + 297675 Pi^2 z^(7/2) + 1102500 z^4 + 297675 Pi^2 z^(9/2) + 396900 z^5 + 99225 Pi^2 z^(11/2)) + (1/(49152 (1 + z)^(17/2))) ((-49152 + 315648 z - 3319680 z^2 - 73112560 z^3 - 378932320 z^4 - 1059791652 z^5 - 1815786382 z^6 - 2018884855 z^7 - 1470112560 z^8 - 679553325 z^9 - 181514970 z^10 - 21391020 z^11) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(49152 (1 + z)^(17/2))) ((49152 - 315648 z + 3319680 z^2 + 73112560 z^3 + 378932320 z^4 + 1059791652 z^5 + 1815786382 z^6 + 2018884855 z^7 + 1470112560 z^8 + 679553325 z^9 + 181514970 z^10 + 21391020 z^11) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (8 - 122 z + 735 z^2 + 11088 z^3 + 25578 z^4 + 22050 z^5 + 6615 z^6) Log[Sqrt[z] + Sqrt[1 + z]])/(1024 Sqrt[z] (1 + z)^(7/2)) + (1/(49152 (1 + z)^(17/2))) ((49152 - 315648 z + 3319680 z^2 + 73112560 z^3 + 378932320 z^4 + 1059791652 z^5 + 1815786382 z^6 + 2018884855 z^7 + 1470112560 z^8 + 679553325 z^9 + 181514970 z^10 + 21391020 z^11) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (99225 z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/1024 + (99225 z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/1024 - (99225 z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/1024

Standard Form

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MathML Form

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2018884855 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1815786382 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1059791652 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 378932320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 73112560 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3319680 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 315648 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 49152 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> 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<power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 6615 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22050 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25578 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11088 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 735 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 122 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]