Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7y9)

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=-5/2, a₃>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=1/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=1/2, b₁=3/2

http://functions.wolfram.com/07.27.03.a7y9.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 1/2}, {3/2, 7/2}, z] == (125 Pi^2)/(8192 Sqrt[-z]) + (Sqrt[1 - z] (135 - 4410 z + 483504 z^2 + 242992 z^3 + 21824 z^4))/ (786432 z^2) - (5 (9 - 300 z - 10400 z^2 - 28800 z^3 - 9600 z^4 - 512 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(262144 (-z)^(5/2)) - (375 Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(4096 Sqrt[-z]) + (375 Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (2048 Sqrt[-z]) + (375 PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (2048 Sqrt[-z]) - (375 PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (2048 Sqrt[-z])

Standard Form

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MathML Form

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<pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <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]