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

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.aqut.01

Input Form

HypergeometricPFQ[{1, 3, 7/2}, {-(7/2), -(7/2)}, z] == (1/(1400 (-1 + z)^14)) (1400 - 18400 z + 114056 z^2 - 406544 z^3 + 7277176 z^4 + 1200262336 z^5 + 18778575816 z^6 + 72700419792 z^7 + 90849024552 z^8 + 37810982352 z^9 + 4458690912 z^10 + 76648062 z^11 - 34965 z^12 - 5670 z^13) + (1287 (2048 z^(9/2) + 93184 z^(11/2) + 768768 z^(13/2) + 1921920 z^(15/2) + 1681680 z^(17/2) + 504504 z^(19/2) + 42042 z^(21/2) + 429 z^(23/2)) ArcSin[Sqrt[z]])/(40 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]