Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9813)

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=4, a₃>=4

For fixed z and a₁=-7/2, a₂=4, a₃=4

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

http://functions.wolfram.com/07.27.03.9813.01

Input Form

HypergeometricPFQ[{-(7/2), 4, 4}, {-(7/2), -(3/2)}, z] == (-768 + 15104 z - 306176 z^2 - 1912161 z^3 - 1469876 z^4 - 154948 z^5)/ (768 (-1 + z)^9) - (1155 (231 z^(5/2) + 594 z^(7/2) + 264 z^(9/2) + 16 z^(11/2)) ArcSin[Sqrt[z]])/(256 Sqrt[1 - z] (-1 + z)^9)

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]