Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.apj8)

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=1, a₃>=1

For fixed z and a₁=1, a₂=1, a₃=7/2

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

http://functions.wolfram.com/07.27.03.apj8.01

Input Form

HypergeometricPFQ[{1, 1, 7/2}, {-(7/2), -(1/2)}, z] == (1/(175 (-1 + z)^9)) (-175 + 1225 z - 630 z^2 - 39060 z^3 + 648774 z^4 + 2467134 z^5 + 781864 z^6 - 31996 z^7 + 1689 z^8) + (9 (4480 z^(9/2) + 6720 z^(11/2) + 1008 z^(13/2) - 56 z^(15/2) + 3 z^(17/2)) ArcSin[Sqrt[z]])/(5 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]