Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a9am)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-3/2, a₃>=-3/2

For fixed z and a₁=-5/2, a₂=-3/2, a₃=3

For fixed z and a₁=-5/2, a₂=-3/2, a₃=3, b₁=7/2

http://functions.wolfram.com/07.27.03.a9am.01

Input Form

HypergeometricPFQ[{-(5/2), -(3/2), 3}, {7/2, 4}, z] == -(16/(4851 z^3)) + (Sqrt[1 - z] (262144 - 523813 z + 2572314 z^2 + 60195512 z^3 + 31084816 z^4 + 508032 z^5))/(79478784 z^3) + (5 (189 - 840 z + 6048 z^2 + 17280 z^3 + 4480 z^4) ArcSin[Sqrt[z]])/ (114688 z^(5/2))

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]