Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a80x)

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=1

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

http://functions.wolfram.com/07.27.03.a80x.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 1}, {1, 4}, z] == (32 (40 - 595 z + 5980 z^2 + 109006 z^3 + 103124 z^4 + 11821 z^5) EllipticE[z])/(800415 Pi z^3) + (32 (-40 + 615 z - 6275 z^2 - 56026 z^3 + 17394 z^4 + 40867 z^5 + 3465 z^6) EllipticK[z])/(800415 Pi z^3)

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]