Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.am7h)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=4, a₃>=4

For fixed z and a₁=-1/2, a₂=4, a₃=4

For fixed z and a₁=-1/2, a₂=4, a₃=4, b₁=3/2

http://functions.wolfram.com/07.27.03.am7h.01

Input Form

HypergeometricPFQ[{-(1/2), 4, 4}, {3/2, 7/2}, -z] == (1/(294912 z^2 (1 + z)^2)) (5 (48 + 304 z + 1350 Pi^2 z^(3/2) + 38804 z^2 + 13725 Pi^2 z^(5/2) + 83800 z^3 + 23400 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2))) + (1/(122880 (1 + z)^(15/2))) ((-226318 - 2324185 z - 8910370 z^2 - 19542740 z^3 - 26483300 z^4 - 22745998 z^5 - 12113650 z^6 - 3662725 z^7 - 481950 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(122880 (1 + z)^(15/2))) ((226318 + 2324185 z + 8910370 z^2 + 19542740 z^3 + 26483300 z^4 + 22745998 z^5 + 12113650 z^6 + 3662725 z^7 + 481950 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (5 (-4 - 28 z + 1215 z^2 + 6685 z^3 + 9025 z^4 + 3675 z^5) Log[Sqrt[z] + Sqrt[1 + z]])/(24576 z^(5/2) (1 + z)^(5/2)) + (1/(122880 (1 + z)^(15/2))) ((226318 + 2324185 z + 8910370 z^2 + 19542740 z^3 + 26483300 z^4 + 22745998 z^5 + 12113650 z^6 + 3662725 z^7 + 481950 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (125 (6 + 49 z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (8192 Sqrt[z]) + (125 (6 + 49 z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/ (8192 Sqrt[z]) - (125 (6 + 49 z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (8192 Sqrt[z])

Standard Form

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MathML Form

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type='integer'> 8910370 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2324185 </cn> <ci> z </ci> </apply> <cn type='integer'> 226318 </cn> </apply> <apply> <ln /> <apply> <times /> <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> <apply> <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'> 125 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 49 </cn> <ci> z 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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]