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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=3, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=4

For fixed z and a₁=3/2, a₂=3, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 3, 4}, {-(5/2), -(1/2)}, z] == (1/(640 (-1 + z)^11)) (-640 - 2176 z + 373376 z^2 - 18116480 z^3 - 294648080 z^4 - 723992720 z^5 - 434936469 z^6 - 56054586 z^7 - 323400 z^8) - (9009 (1584 z^(7/2) + 10384 z^(9/2) + 15359 z^(11/2) + 6084 z^(13/2) + 504 z^(15/2)) ArcSin[Sqrt[z]])/ (128 Sqrt[1 - z] (-1 + 11 z - 55 z^2 + 165 z^3 - 330 z^4 + 462 z^5 - 462 z^6 + 330 z^7 - 165 z^8 + 55 z^9 - 11 z^10 + z^11))

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]