Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amm1)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.amm1.01

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(9/2), 3}, z] == -((1/10418625) (8 E^(z/2) (-1454355 + 2534490 z - 2853900 z^2 + 3156300 z^3 - 4611600 z^4 + 16829568 z^5 + 50754816 z^6 + 32313600 z^7 + 8250624 z^8 + 972288 z^9 + 52224 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(10418625 z)) (4 E^(z/2) (1216215 + 561330 z - 2479680 z^2 + 3099600 z^3 - 3288600 z^4 + 4013856 z^5 - 7676928 z^6 + 56567808 z^7 + 50745600 z^8 + 14707200 z^9 + 1843200 z^10 + 102400 z^11 + 2048 z^12) 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]