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

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, a₃>=3

For fixed z and a₁=1, a₂=3, a₃=7/2

For fixed z and a₁=1, a₂=3, a₃=7/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1, 3, 7/2}, {-(5/2), -(5/2)}, -z] == (1/(200 (1 + z)^12)) (200 + 2064 z + 11856 z^2 - 241600 z^3 + 39232248 z^4 - 422238960 z^5 + 1036513632 z^6 - 714776832 z^7 + 126409360 z^8 - 3053736 z^9 - 735 z^10 + 490 z^11) + (693 (1024 z^(7/2) - 33792 z^(9/2) + 190080 z^(11/2) - 295680 z^(13/2) + 138600 z^(15/2) - 16632 z^(17/2) + 231 z^(19/2)) ArcSinh[Sqrt[z]])/ (40 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]