Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ah63)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=2, a₃>=2

For fixed z and a₁=-3/2, a₂=2, a₃=2

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

http://functions.wolfram.com/07.27.03.ah63.01

Input Form

HypergeometricPFQ[{-(3/2), 2, 2}, {3/2, 5/2}, -z] == (96 + 72 Pi^2 Sqrt[z] + 1096 z + 324 Pi^2 z^(3/2) + 900 z^2 + 225 Pi^2 z^(5/2))/(2048 z) + ((-2680 - 11948 z - 23743 z^2 - 24030 z^3 - 12225 z^4 - 2490 z^5) Log[1 + Sqrt[z] - Sqrt[1 + z]])/(512 (1 + z)^(7/2)) + ((2680 + 11948 z + 23743 z^2 + 24030 z^3 + 12225 z^4 + 2490 z^5) Log[1 - Sqrt[z] + Sqrt[1 + z]])/(512 (1 + z)^(7/2)) + (3 Sqrt[1 + z] (-8 + 58 z + 75 z^2) Log[Sqrt[z] + Sqrt[1 + z]])/ (512 z^(3/2)) + ((2680 + 11948 z + 23743 z^2 + 24030 z^3 + 12225 z^4 + 2490 z^5) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (512 (1 + z)^(7/2)) + (9 (8 + 36 z + 25 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (512 Sqrt[z]) + (9 (8 + 36 z + 25 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(512 Sqrt[z]) - (9 (8 + 36 z + 25 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(512 Sqrt[z])

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 25 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <ci> z </ci> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <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> 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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]