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

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=5/2, a₃>=5/2

For fixed z and a₁=1, a₂=5/2, a₃=4

For fixed z and a₁=1, a₂=5/2, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1, 5/2, 4}, {-(7/2), -(3/2)}, z] == (1/(336 (-1 + z)^12)) (336 - 3392 z + 23456 z^2 - 461760 z^3 + 21045680 z^4 + 380423296 z^5 + 1066557888 z^6 + 752509296 z^7 + 121302720 z^8 + 1084545 z^9 - 6090 z^10 - 840 z^11) + (2145 (1920 z^(9/2) + 14080 z^(11/2) + 23760 z^(13/2) + 11088 z^(15/2) + 1155 z^(17/2)) ArcSin[Sqrt[z]])/(16 Sqrt[1 - z] (1 - 12 z + 66 z^2 - 220 z^3 + 495 z^4 - 792 z^5 + 924 z^6 - 792 z^7 + 495 z^8 - 220 z^9 + 66 z^10 - 12 z^11 + 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]