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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{-(1/2), 11/2}, {-(7/2), 2}, z] == (1/99225) (E^(z/2) (99225 - 18900 z - 32760 z^2 + 28080 z^3 - 21552 z^4 - 17664 z^5 - 2880 z^6 - 128 z^7) BesselI[0, z/2]) + (1/99225) (E^(z/2) (33075 + 44100 z - 59400 z^2 + 30768 z^3 - 7824 z^4 - 14976 z^5 - 2752 z^6 - 128 z^7) 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]