Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2762)

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=-7/2, a₂>=-7/2

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

For fixed z and a₁=-7/2, a₂=-5/2, a₃=1

For fixed z and a₁=-7/2, a₂=-5/2, a₃=1, b₁=5/2

http://functions.wolfram.com/07.27.03.2762.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 1}, {5/2, 4}, z] == -((2 (-8 + 572 z + 14157 z^2))/(99099 z^3)) + (1/(202954752 z^3)) (Sqrt[1 - z] (-32768 + 2326528 z + 48740845 z^2 + 142636550 z^3 + 97783592 z^4 + 13996784 z^5 + 88704 z^6)) + (5 (231 + 1848 z + 3168 z^2 + 1408 z^3 + 128 z^4) ArcSin[Sqrt[z]])/ (22528 z^(3/2))

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]