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

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=1/2, a₃>=1/2

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

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

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

Input Form

HypergeometricPFQ[{1/2, 1/2, 7/2}, {-(5/2), 4}, -z] == (32 (1848 + 4557 z + 3171 z^2 + 326 z^3 + 32 z^4 + 128 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (375 Pi z^3 (1 + z)^3) + (32 (1848 + 4557 z + 3171 z^2 + 326 z^3 + 32 z^4 + 128 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (375 Pi z^3 (1 + z)^(5/2)) - (128 (462 + 735 z + 183 z^2 - 16 z^3 + 64 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (375 Pi z^3 (1 + z)^2) + (64 (-924 - 2163 z - 1335 z^2 + 8 z^3 + 64 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (375 Pi z^3 (1 + z)^(5/2))

Standard Form

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MathML Form

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</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]