Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aos2)

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=3, a₃>=3

For fixed z and a₁=1/2, a₂=3, a₃=7/2

For fixed z and a₁=1/2, a₂=3, a₃=7/2, b₁=-7/2

http://functions.wolfram.com/07.27.03.aos2.01

Input Form

HypergeometricPFQ[{1/2, 3, 7/2}, {-(7/2), -(7/2)}, z] == (1/(175 (1 - z)^3 (-1 + z)^11)) (-175 + 2375 z - 15037 z^2 + 57493 z^3 - 364742 z^4 - 39230282 z^5 - 603765162 z^6 - 2262922662 z^7 - 2696429307 z^8 - 1037439117 z^9 - 106191657 z^10 - 1288287 z^11)

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]