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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

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

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

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(7/2), -(3/2)}, -z] == (1/(768 (1 + z)^16)) (768 + 4096 z + 329728 z^2 + 37785600 z^3 + 4004172800 z^4 - 180577270528 z^5 + 1506504257664 z^6 - 4273681294688 z^7 + 4853219902960 z^8 - 2278711730790 z^9 + 416427581229 z^10 - 24472007472 z^11 + 272324844 z^12) - (15015 (549120 z^(9/2) - 10175360 z^(11/2) + 53294880 z^(13/2) - 107260176 z^(15/2) + 91365010 z^(17/2) - 33020955 z^(19/2) + 4665870 z^(21/2) - 207240 z^(23/2) + 1584 z^(25/2)) ArcSinh[Sqrt[z]])/ (256 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'> 1820 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </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]