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

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=3, a₃>=3

For fixed z and a₁=-1/2, a₂=3, a₃=4

For fixed z and a₁=-1/2, a₂=3, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{-(1/2), 3, 4}, {-(7/2), 1/2}, z] == (-896 + 6672 z - 15352 z^2 - 30490 z^3 + 553725 z^4 + 248674 z^5 + 3432 z^6)/ (896 (-1 + z)^9) + (15 (-16 Sqrt[z] + 152 z^(3/2) - 646 z^(5/2) + 1615 z^(7/2) + 5044 z^(9/2) + 1144 z^(11/2)) ArcSin[Sqrt[z]])/ (128 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]