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

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=3/2, a₃>=3/2

For fixed z and a₁=1, a₂=3/2, a₃=2

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

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

Input Form

HypergeometricPFQ[{1, 3/2, 2}, {-(7/2), 7/2}, z] == (-23040 + 90240 z - 131954 z^2 + 85328 z^3 - 20784 z^4 + 315 z^5)/ (14 (-1 + z)^4 z^2) - (15 (-1536 + 7040 z - 12672 z^2 + 11088 z^3 - 4620 z^4 + 693 z^5) ArcSin[Sqrt[z]])/(14 Sqrt[1 - z] (-1 + z)^4 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]