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

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=-7/2

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

Input Form

HypergeometricPFQ[{1, 3, 7/2}, {-(7/2), -(1/2)}, z] == (1/(40 (-1 + z)^11)) (-40 + 200 z + 3896 z^2 - 86856 z^3 + 1999008 z^4 + 16319952 z^5 + 20054320 z^6 + 5192032 z^7 + 166048 z^8 + 99 z^9 - 54 z^10) + (9009 (128 z^(9/2) + 448 z^(11/2) + 336 z^(13/2) + 56 z^(15/2) + z^(17/2)) ArcSin[Sqrt[z]])/ (8 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]