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

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=7/2, a₃>=7/2

For fixed z and a₁=3/2, a₂=7/2, a₃=7/2

For fixed z and a₁=3/2, a₂=7/2, a₃=7/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 7/2, 7/2}, {-(5/2), 1}, z] == (1/(75 Pi (-1 + z)^10)) (4 (95 - 1584 z + 16594 z^2 - 295764 z^3 - 1109025 z^4 - 623700 z^5 - 51000 z^6) EllipticE[z]) + (1/(75 Pi (-1 + z)^9)) (2 (115 - 1828 z + 19074 z^2 - 395820 z^3 - 1151325 z^4 - 505800 z^5 - 28800 z^6) EllipticK[z])

Standard Form

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MathML Form

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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]