Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3112)

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=5/2

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

http://functions.wolfram.com/07.27.03.3112.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 5/2}, {3/2, 3}, -z] == -((32 (-5 + 125 z - 16362 z^2 + 49538 z^3 - 18737 z^4 + 225 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(93555 Pi z^2)) - (1/(93555 Pi z^2)) (32 Sqrt[1 + z] (-5 + 125 z - 16362 z^2 + 49538 z^3 - 18737 z^4 + 225 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) - (32 Sqrt[1 + z] (5 - 11820 z + 70302 z^2 - 73772 z^3 + 14085 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(93555 Pi z^2) + (32 (-5 - 11570 z + 37578 z^2 + 25304 z^3 - 23389 z^4 + 450 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(93555 Pi z^2)

Standard Form

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MathML Form

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</ci> <cn type='integer'> 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]