Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ajm5)

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=3

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

http://functions.wolfram.com/07.27.03.ajm5.01

Input Form

HypergeometricPFQ[{-(1/2), 1/2, 3}, {-(7/2), -(7/2)}, z] == (-1225 + 12325 z - 55857 z^2 + 150245 z^3 - 263315 z^4 + 529815 z^5 + 920205 z^6 + 1288287 z^7)/(1225 (1 - z)^3 (-1 + z)^7)

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]