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

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=3, a₃>=3

For fixed z and a₁=1/2, a₂=3, a₃=4

For fixed z and a₁=1/2, a₂=3, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1/2, 3, 4}, {-(7/2), -(5/2)}, z] == (1/(4480 (-1 + z)^13)) (-4480 + 55168 z - 321792 z^2 + 791808 z^3 + 62252928 z^4 + 2826330048 z^5 + 16758216688 z^6 + 26103384632 z^7 + 11617478301 z^8 + 1188145530 z^9 + 5549544 z^10) + (1287 (9152 z^(9/2) + 141648 z^(11/2) + 486600 z^(13/2) + 499655 z^(15/2) + 152724 z^(17/2) + 10296 z^(19/2)) ArcSin[Sqrt[z]])/ (128 Sqrt[1 - z] (-1 + 13 z - 78 z^2 + 286 z^3 - 715 z^4 + 1287 z^5 - 1716 z^6 + 1716 z^7 - 1287 z^8 + 715 z^9 - 286 z^10 + 78 z^11 - 13 z^12 + z^13))

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]