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

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=2, a₂>=2

For fixed z and a₁=2, a₂=5/2, a₃>=5/2

For fixed z and a₁=2, a₂=5/2, a₃=3

For fixed z and a₁=2, a₂=5/2, a₃=3, b₁=-5/2

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

Input Form

HypergeometricPFQ[{2, 5/2, 3}, {-(5/2), -(5/2)}, z] == (1/(80 (-1 + z)^12)) (80 - 768 z + 4768 z^2 + 188608 z^3 + 30355632 z^4 + 353714240 z^5 + 969412224 z^6 + 791261856 z^7 + 188058486 z^8 + 9466779 z^9 + 13230 z^10) + (693 (768 z^(7/2) + 27008 z^(9/2) + 165440 z^(11/2) + 290400 z^(13/2) + 164010 z^(15/2) + 27489 z^(17/2) + 924 z^(19/2)) 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]