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

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.alsj.01

Input Form

HypergeometricPFQ[{-(1/2), 3, 7/2}, {-(7/2), -(7/2)}, z] == (1/(175 (1 - z)^3 (-1 + z)^10)) (175 - 2350 z + 14571 z^2 - 55528 z^3 + 114478 z^4 - 4600596 z^5 - 47777730 z^6 - 118942824 z^7 - 76678173 z^8 - 11410542 z^9 - 184041 z^10)

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]