Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ao40)

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=2, a₃>=2

For fixed z and a₁=1/2, a₂=2, a₃=3

For fixed z and a₁=1/2, a₂=2, a₃=3, b₁=-7/2

http://functions.wolfram.com/07.27.03.ao40.01

Input Form

HypergeometricPFQ[{1/2, 2, 3}, {-(7/2), -(7/2)}, z] == (1/(19600 (-1 + z)^12)) (19600 - 230400 z + 1242912 z^2 - 4026944 z^3 + 13863792 z^4 + 673627200 z^5 + 7091819200 z^6 + 16158756768 z^7 + 9868717584 z^8 + 1325333163 z^9 + 8004150 z^10) + (1287 (1408 z^(9/2) + 44800 z^(11/2) + 239200 z^(13/2) + 343200 z^(15/2) + 139425 z^(17/2) + 12012 z^(19/2)) ArcSin[Sqrt[z]])/ (560 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]