Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.avb0)

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.avb0.01

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(7/2), -(1/2)}, z] == (1/(256 (-1 + z)^15)) (-256 - 4352 z + 464640 z^2 - 17086720 z^3 + 893102848 z^4 + 22018168704 z^5 + 106186179008 z^6 + 173259046480 z^7 + 107694898200 z^8 + 24852686217 z^9 + 1792671132 z^10 + 24167124 z^11) + (45045 (91520 z^(9/2) + 985920 z^(11/2) + 3061872 z^(13/2) + 3580072 z^(15/2) + 1667403 z^(17/2) + 292194 z^(19/2) + 15720 z^(21/2) + 144 z^(23/2)) ArcSin[Sqrt[z]])/(256 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'> 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> </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]