Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au97)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=3

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

http://functions.wolfram.com/07.27.03.au97.01

Input Form

HypergeometricPFQ[{5/2, 3, 3}, {-(7/2), -(5/2)}, z] == (1/(2240 (-1 + z)^14)) (2240 - 25600 z + 166208 z^2 + 1257088 z^3 - 451825472 z^4 - 26722610432 z^5 - 232253216832 z^6 - 595908977664 z^7 - 537621502704 z^8 - 171332885724 z^9 - 16582808319 z^10 - 298288914 z^11) - (1287 (73216 z^(9/2) + 1559168 z^(11/2) + 8006016 z^(13/2) + 13994640 z^(15/2) + 9150900 z^(17/2) + 2162853 z^(19/2) + 153384 z^(21/2) + 1848 z^(23/2)) ArcSin[Sqrt[z]])/ (64 Sqrt[1 - z] (1 - 14 z + 91 z^2 - 364 z^3 + 1001 z^4 - 2002 z^5 + 3003 z^6 - 3432 z^7 + 3003 z^8 - 2002 z^9 + 1001 z^10 - 364 z^11 + 91 z^12 - 14 z^13 + z^14))

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]