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

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.aqux.01

Input Form

HypergeometricPFQ[{1, 3, 7/2}, {-(7/2), -(3/2)}, z] == (1/(40 (-1 + z)^12)) (40 - 400 z + 2832 z^2 - 59584 z^3 + 2781592 z^4 + 51329520 z^5 + 148489440 z^6 + 110984544 z^7 + 20597832 z^8 + 513654 z^9 - 75 z^10 - 90 z^11) + (9009 (256 z^(9/2) + 1920 z^(11/2) + 3360 z^(13/2) + 1680 z^(15/2) + 210 z^(17/2) + 3 z^(19/2)) ArcSin[Sqrt[z]])/ (8 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]