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

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=7/2

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

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

Input Form

HypergeometricPFQ[{1, 3/2, 7/2}, {-(7/2), -(7/2)}, z] == (1/(35 (1 - z) (-1 + z)^12)) (35 - 440 z + 2562 z^2 - 8960 z^3 + 46865 z^4 + 4084080 z^5 + 53633580 z^6 + 164996832 z^7 + 151602165 z^8 + 39279240 z^9 + 1629810 z^10 - 30240 z^11 + 567 z^12)

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]