Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3254)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.3254.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 3}, {7/2, 7/2}, z] == (-12810 + 134680 z + 5780779 z^2 + 8712585 z^3 + 2013585 z^4 + 17325 z^5)/ (8388608 z^2) + (105 (-62 + 710 z - 16125 z^2 - 22000 z^3 + 25750 z^4 + 11562 z^5 + 165 z^6) Log[1 - Sqrt[z]])/(16777216 z^(5/2)) - (105 (-62 + 710 z - 16125 z^2 - 22000 z^3 + 25750 z^4 + 11562 z^5 + 165 z^6) Log[1 + Sqrt[z]])/(16777216 z^(5/2)) - (1575 (1 - 10 z + 150 z^2 + 1000 z^3 + 875 z^4 + 126 z^5) PolyLog[2, -Sqrt[z]])/(4194304 z^(5/2)) + (1575 (1 - 10 z + 150 z^2 + 1000 z^3 + 875 z^4 + 126 z^5) PolyLog[2, Sqrt[z]])/(4194304 z^(5/2))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 150 </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'> 10 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4194304 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </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]