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

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=2

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

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

Input Form

HypergeometricPFQ[{3/2, 2, 2}, {-(7/2), 7/2}, z] == (-69120 + 336000 z - 648092 z^2 + 616732 z^3 - 285908 z^4 + 49443 z^5)/ (28 (-1 + z)^5 z^2) + (15 (4608 - 25472 z + 57728 z^2 - 68112 z^3 + 43428 z^4 - 13629 z^5 + 1386 z^6) ArcSin[Sqrt[z]])/ (28 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]