Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.at1c)

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=2, a₂>=2

For fixed z and a₁=2, a₂=2, a₃>=2

For fixed z and a₁=2, a₂=2, a₃=3

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

http://functions.wolfram.com/07.27.03.at1c.01

Input Form

HypergeometricPFQ[{2, 2, 3}, {-(7/2), 4}, z] == (-135135 + 765765 z - 1780709 z^2 + 2155245 z^3 - 1403307 z^4 + 438455 z^5 - 29919 z^6)/(70 (-1 + z)^6 z^2) - (1/(70 Sqrt[1 - z] (-1 + z)^6 z^(5/2))) (3 (-90090 + 570570 z - 1519518 z^2 + 2187042 z^3 - 1808378 z^4 + 829582 z^5 - 176138 z^6 + 3465 z^7) ArcSin[Sqrt[z]]) - (3861 ArcSin[Sqrt[z]]^2)/(2 z^3)

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]