Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8bc)

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=5/2

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

http://functions.wolfram.com/07.27.03.a8bc.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 5/2}, {3/2, 4}, -z] == (32 (120 + 575 z - 6260 z^2 + 374298 z^3 - 574412 z^4 + 91103 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(2401245 Pi z^3) + (1/(2401245 Pi z^3)) (32 Sqrt[1 + z] (120 + 575 z - 6260 z^2 + 374298 z^3 - 574412 z^4 + 91103 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) - (1/(2401245 Pi z^3)) (256 Sqrt[1 + z] (15 + 70 z - 38310 z^2 + 135216 z^3 - 81121 z^4 + 6930 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(2401245 Pi z^3)) (64 (60 + 295 z + 146980 z^2 - 166566 z^3 - 249928 z^4 + 63383 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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<cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2401245 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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]