Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au95)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=3

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

http://functions.wolfram.com/07.27.03.au95.01

Input Form

HypergeometricPFQ[{5/2, 3, 3}, {-(7/2), -(7/2)}, z] == (1/(15680 (-1 + z)^15)) (-15680 + 206400 z - 1343424 z^2 + 3895360 z^3 - 415369920 z^4 - 95665133760 z^5 - 1899564067520 z^6 - 9873817821504 z^7 - 17983070614080 z^8 - 12511672584840 z^9 - 3225661278840 z^10 - 260125640775 z^11 - 3960999042 z^12) - (1287 (146432 z^(9/2) + 8213504 z^(11/2) + 87015296 z^(13/2) + 296095488 z^(15/2) + 385396440 z^(17/2) + 199821336 z^(19/2) + 38915877 z^(21/2) + 2330328 z^(23/2) + 24024 z^(25/2)) ArcSin[Sqrt[z]])/ (448 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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type='integer'> 3003 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1365 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 455 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <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> </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]