Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.adjg)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=7/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.adjg.01

Input Form

HypergeometricPFQ[{1/2, 7/2}, {-(11/2), 4}, z] == (1/(51975 z)) (4 E^(z/2) (-2297295 + 1330560 z - 476280 z^2 + 128400 z^3 - 28080 z^4 + 5184 z^5 - 832 z^6 + 128 z^7) BesselI[0, z/2]) + (1/(51975 z^2)) (4 E^(z/2) (9189180 - 5270265 z + 2162160 z^2 - 672360 z^3 + 167760 z^4 - 34896 z^5 + 6208 z^6 - 960 z^7 + 128 z^8) BesselI[1, 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,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]