Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ak7j)

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=1, a₃>=1

For fixed z and a₁=-1/2, a₂=1, a₃=3

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

http://functions.wolfram.com/07.27.03.ak7j.01

Input Form

HypergeometricPFQ[{-(1/2), 1, 3}, {-(7/2), -(5/2)}, z] == (1/(1400 (-1 + z)^9)) (-1400 + 12840 z - 52432 z^2 + 126368 z^3 - 280272 z^4 - 1215272 z^5 - 2287092 z^6 - 138915 z^7 + 7350 z^8) - (1287 (8 z^(9/2) + 44 z^(11/2) + 33 z^(13/2)) ArcSin[Sqrt[z]])/ (40 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]