Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a9ca)

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=-3/2, a₃>=-3/2

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

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

http://functions.wolfram.com/07.27.03.a9ca.01

Input Form

HypergeometricPFQ[{-(5/2), -(3/2), 7/2}, {-(1/2), 3}, z] == -((16 (10 + 97 z - 3627 z^2 + 30712 z^3 + 4480 z^4) EllipticE[z])/ (11025 Pi z^2)) - (32 (-5 - 46 z + 1149 z^2 - 10058 z^3 + 8960 z^4) EllipticK[z])/(11025 Pi z^2)

Standard Form

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MathML Form

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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]