Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.alp6)

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=3

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

http://functions.wolfram.com/07.27.03.alp6.01

Input Form

HypergeometricPFQ[{-(1/2), 3, 3}, {-(7/2), -(7/2)}, z] == (1/(78400 (-1 + z)^12)) (78400 - 969600 z + 5501568 z^2 - 19030016 z^3 + 35940288 z^4 - 1129832400 z^5 - 9304362200 z^6 - 17240323698 z^7 - 7022807649 z^8 - 461321718 z^9) - (1287 (2288 z^(9/2) + 65000 z^(11/2) + 294950 z^(13/2) + 328575 z^(15/2) + 85800 z^(17/2) + 3432 z^(19/2)) ArcSin[Sqrt[z]])/ (2240 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]