Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a84x)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.a84x.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3/2}, {3, 3}, z] == (512 (12835 + 76040 z + 419634 z^2 + 251378 z^3 + 21124 z^4) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/(6251175 Pi^2 z^2) - (1/(6251175 Pi^2 z^2)) (512 Sqrt[1 - z] (9685 + 45780 z + 173124 z^2 + 82289 z^3 + 5040 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(6251175 Pi^2 z^2)) (512 (12835 + 76040 z + 419634 z^2 + 251378 z^3 + 21124 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(6251175 Pi^2 z^2)) (256 Sqrt[1 - z] (9685 + 45780 z + 173124 z^2 + 82289 z^3 + 5040 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (256 (9685 + 41725 z + 255294 z^2 + 146567 z^3 + 11822 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(6251175 Pi^2 z^2)

Standard Form

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MathML Form

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-1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 6251175 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 11822 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 146567 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 255294 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 41725 </cn> <ci> z </ci> </apply> <cn type='integer'> 9685 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep 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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]