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

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=3

For fixed z and a₁=2, a₂=5/2, a₃=3, b₁=-7/2

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

Input Form

HypergeometricPFQ[{2, 5/2, 3}, {-(7/2), -(7/2)}, -z] == (1/(3920 (1 + z)^14)) (3920 + 50080 z + 305648 z^2 + 1000832 z^3 + 36115408 z^4 - 6755707168 z^5 + 111303764208 z^6 - 462637471296 z^7 + 639389418096 z^8 - 310945010376 z^9 + 48414822456 z^10 - 1687547631 z^11 + 1600830 z^12) + (1287 (-11264 z^(9/2) + 535552 z^(11/2) - 4677504 z^(13/2) + 12629760 z^(15/2) - 12338040 z^(17/2) + 4396392 z^(19/2) - 501501 z^(21/2) + 12012 z^(23/2)) ArcSinh[Sqrt[z]])/ (112 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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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2002 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1001 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14 </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]