Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av06)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

For fixed z and a₁=3, a₂=7/2, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.av06.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(7/2), -(5/2)}, z] == (1/(640 (-1 + z)^16)) (640 - 7168 z + 64512 z^2 + 2123776 z^3 - 777402880 z^4 - 63947074560 z^5 - 814407254528 z^6 - 3281421889408 z^7 - 5135154682944 z^8 - 3312380334120 z^9 - 852438641340 z^10 - 75745982169 z^11 - 1561210794 z^12 - 792792 z^13) - (9009 (146432 z^(9/2) + 4372992 z^(11/2) + 33217152 z^(13/2) + 92377792 z^(15/2) + 106731768 z^(17/2) + 52545636 z^(19/2) + 10432851 z^(21/2) + 705276 z^(23/2) + 10296 z^(25/2)) ArcSin[Sqrt[z]])/ (128 Sqrt[1 - z] (1 - 16 z + 120 z^2 - 560 z^3 + 1820 z^4 - 4368 z^5 + 8008 z^6 - 11440 z^7 + 12870 z^8 - 11440 z^9 + 8008 z^10 - 4368 z^11 + 1820 z^12 - 560 z^13 + 120 z^14 - 16 z^15 + z^16))

Standard Form

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MathML Form

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type='integer'> 120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn 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]