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

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=2, a₃>=2

For fixed z and a₁=-1/2, a₂=2, a₃=4

For fixed z and a₁=-1/2, a₂=2, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{-(1/2), 2, 4}, {-(7/2), -(3/2)}, z] == (1/(672 (-1 + z)^10)) (672 - 7232 z + 33824 z^2 - 63744 z^3 - 829120 z^4 - 8113238 z^5 - 5404377 z^6 - 172788 z^7 + 6468 z^8) - (2145 (66 z^(9/2) + 191 z^(11/2) + 66 z^(13/2)) ArcSin[Sqrt[z]])/ (32 Sqrt[1 - z] (-1 + 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]