Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5897)

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=1/2, a₃>=1/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=1

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

http://functions.wolfram.com/07.27.03.5897.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 1}, {3, 4}, z] == -((8 (8 + 33 z))/(99 z^2)) + (256 (693 + 61244 z + 152558 z^2 + 17772 z^3 - 3403 z^4 + 560 z^5 - 48 z^6) EllipticE[z])/(4459455 Pi z^3) + (256 (-693 - 38375 z - 34618 z^2 + 72210 z^3 + 1735 z^4 - 283 z^5 + 24 z^6) EllipticK[z])/(4459455 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]