Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aq5x)

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, a₂>=1

For fixed z and a₁=1, a₂=2, a₃>=2

For fixed z and a₁=1, a₂=2, a₃=2

For fixed z and a₁=1, a₂=2, a₃=2, b₁=-5/2

http://functions.wolfram.com/07.27.03.aq5x.01

Input Form

HypergeometricPFQ[{1, 2, 2}, {-(5/2), 4}, z] == (10395 - 29610 z + 27668 z^2 - 8438 z^3 + 105 z^4)/(10 (-1 + z)^3 z^2) - (3 (3465 - 12180 z + 15498 z^2 - 8244 z^3 + 1441 z^4) ArcSin[Sqrt[z]])/ (5 Sqrt[1 - z] (-1 + z)^3 z^(5/2)) + (189 (-11 + 2 z) 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]