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

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=4

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

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

Input Form

HypergeometricPFQ[{1/2, 1, 4}, {-(7/2), 7/2}, z] == (1920 - 8320 z + 13232 z^2 - 8344 z^3 + 147 z^4 + 1890 z^5 - 840 z^6)/ (112 (-1 + z)^5 z^2) - (15 (128 - 640 z + 1248 z^2 - 1144 z^3 + 429 z^4) ArcSin[Sqrt[z]])/(112 Sqrt[1 - z] (-1 + z)^5 z^(5/2))

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]