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

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.aoor.01

Input Form

HypergeometricPFQ[{1/2, 3, 3}, {-(7/2), -(7/2)}, z] == (1/(78400 (-1 + z)^13)) (-78400 + 990400 z - 5796096 z^2 + 20382848 z^3 - 109988288 z^4 - 9660569664 z^5 - 122223395200 z^6 - 358366939424 z^7 - 309786336288 z^8 - 74912599047 z^9 - 3383846466 z^10) - (1287 (18304 z^(9/2) + 688896 z^(11/2) + 4514400 z^(13/2) + 8434400 z^(15/2) + 4987125 z^(17/2) + 833976 z^(19/2) + 24024 z^(21/2)) ArcSin[Sqrt[z]])/(2240 Sqrt[1 - z] (-1 + 13 z - 78 z^2 + 286 z^3 - 715 z^4 + 1287 z^5 - 1716 z^6 + 1716 z^7 - 1287 z^8 + 715 z^9 - 286 z^10 + 78 z^11 - 13 z^12 + z^13))

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]