Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1765)

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=-7/2, a₃>=-7/2

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

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

http://functions.wolfram.com/07.27.03.1765.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 2}, {5/2, 7/2}, z] == (3675 + 158515 z + 7395575 z^2 + 15351749 z^3 + 6413120 z^4 + 430710 z^5)/ (10485760 z^2) + (147 (5 + 94 z - 2750 z^2 - 6000 z^3 + 3875 z^4 + 4370 z^5 + 406 z^6) Log[1 - Sqrt[z]])/(4194304 z^(5/2)) - (147 (5 + 94 z - 2750 z^2 - 6000 z^3 + 3875 z^4 + 4370 z^5 + 406 z^6) Log[1 + Sqrt[z]])/(4194304 z^(5/2)) - (2205 (-2 + 25 z + 200 z^2 + 250 z^3 + 70 z^4 + 3 z^5) PolyLog[2, -Sqrt[z]])/(1048576 z^(3/2)) + (2205 (-2 + 25 z + 200 z^2 + 250 z^3 + 70 z^4 + 3 z^5) PolyLog[2, Sqrt[z]])/ (1048576 z^(3/2))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25 </cn> <ci> z </ci> </apply> <cn type='integer'> -2 </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'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <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]