Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ar2d)

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=7/2, a₃>=7/2

For fixed z and a₁=1, a₂=7/2, a₃=4

For fixed z and a₁=1, a₂=7/2, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.ar2d.01

Input Form

HypergeometricPFQ[{1, 7/2, 4}, {-(7/2), -(5/2)}, z] == (1/(80 (-1 + z)^14)) (80 - 992 z + 6256 z^2 + 5568 z^3 - 6519856 z^4 - 357019936 z^5 - 2789875088 z^6 - 6210272640 z^7 - 4576757328 z^8 - 1062035832 z^9 - 56204772 z^10 - 94983 z^11 + 966 z^12 - 168 z^13) - (9009 (1024 z^(9/2) + 19968 z^(11/2) + 91520 z^(13/2) + 137280 z^(15/2) + 72072 z^(17/2) + 12012 z^(19/2) + 429 z^(21/2)) ArcSin[Sqrt[z]])/ (16 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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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]