Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av18)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

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

http://functions.wolfram.com/07.27.03.av18.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(3/2), -(1/2)}, z] == (1/(128 (-1 + z)^12)) (128 + 5632 z - 1367808 z^2 - 69375872 z^3 - 498108160 z^4 - 997866144 z^5 - 644318136 z^6 - 126126861 z^7 - 5312034 z^8 - 5880 z^9) - (3465 (2688 z^(5/2) + 48768 z^(7/2) + 204640 z^(9/2) + 275400 z^(11/2) + 126315 z^(13/2) + 17724 z^(15/2) + 504 z^(17/2)) ArcSin[Sqrt[z]])/ (128 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]