Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.atg9)

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=2, a₂>=2

For fixed z and a₁=2, a₂=5/2, a₃>=5/2

For fixed z and a₁=2, a₂=5/2, a₃=4

For fixed z and a₁=2, a₂=5/2, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.atg9.01

Input Form

HypergeometricPFQ[{2, 5/2, 4}, {-(7/2), -(7/2)}, -z] == (1/(1568 (1 + z)^15)) (1568 + 20960 z + 136992 z^2 + 433888 z^3 + 32640160 z^4 - 7273621152 z^5 + 140577345440 z^6 - 705099015712 z^7 + 1222438300512 z^8 - 790318917960 z^9 + 180040060200 z^10 - 11111406075 z^11 + 39273696 z^12 + 213444 z^13) + (6435 (-11264 z^(9/2) + 617472 z^(11/2) - 6353280 z^(13/2) + 20800000 z^(15/2) - 25654200 z^(17/2) + 12262536 z^(19/2) - 2075073 z^(21/2) + 90090 z^(23/2)) ArcSinh[Sqrt[z]])/ (224 Sqrt[1 + z] (1 + 15 z + 105 z^2 + 455 z^3 + 1365 z^4 + 3003 z^5 + 5005 z^6 + 6435 z^7 + 6435 z^8 + 5005 z^9 + 3003 z^10 + 1365 z^11 + 455 z^12 + 105 z^13 + 15 z^14 + z^15))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 15 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]