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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=2, a₃>=2

For fixed z and a₁=3/2, a₂=2, a₃=3

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

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

Input Form

HypergeometricPFQ[{3/2, 2, 3}, {-(7/2), 7/2}, z] == (-69120 + 401280 z - 961552 z^2 + 1209840 z^3 - 831084 z^4 + 281821 z^5 - 20790 z^6)/(112 (-1 + z)^6 z^2) + (15 (4608 - 29824 z + 81536 z^2 - 121264 z^3 + 104676 z^4 - 51051 z^5 + 12012 z^6) ArcSin[Sqrt[z]])/(112 Sqrt[1 - z] (-1 + z)^6 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]