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

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=7/2, a₃>=7/2

For fixed z and a₁=1/2, a₂=7/2, a₃=7/2

For fixed z and a₁=1/2, a₂=7/2, a₃=7/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1/2, 7/2, 7/2}, {-(5/2), 2}, -z] == (4 (-21 - 124 z - 158 z^2 + 1020 z^3 + 12363 z^4 - 3048 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (75 Pi z (1 + z)^8) + (4 (-21 - 124 z - 158 z^2 + 1020 z^3 + 12363 z^4 - 3048 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (75 Pi z (1 + z)^(15/2)) + (8 (-27 - 265 z - 1305 z^2 - 6147 z^3 + 2088 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (75 Pi z (1 + z)^7) + (128 (3 + 26 z + 108 z^2 + 402 z^3 - 519 z^4 + 60 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (75 Pi z (1 + z)^(15/2))

Standard Form

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MathML Form

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<apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 15 <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]