Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2840)

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=3/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3/2, b₁=-1/2

http://functions.wolfram.com/07.27.03.2840.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 3/2}, {-(1/2), 3}, -z] == (16 (50 + 235 z + 3141 z^2 + 31201 z^3 - 33499 z^4 + 720 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(10395 Pi z^2) + (1/(10395 Pi z^2)) (16 Sqrt[1 + z] (50 + 235 z + 3141 z^2 + 31201 z^3 - 33499 z^4 + 720 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (32 Sqrt[1 + z] (-25 + 1185 z + 10137 z^2 - 39317 z^3 + 14220 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(10395 Pi z^2) - (32 (25 + 1420 z + 13278 z^2 - 8116 z^3 - 19279 z^4 + 720 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(10395 Pi z^2)

Standard Form

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MathML Form

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</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]