Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa2j)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.aa2j.01

Input Form

HypergeometricPFQ[{-(3/2), 9/2}, {-(11/2), 1}, z] == (1/363825) (E^(z/2) (363825 + 264600 z - 235200 z^2 + 42000 z^3 + 16800 z^4 - 13120 z^5 + 6400 z^6 + 2176 z^7 + 128 z^8) BesselI[0, z/2]) + (1/363825) (8 E^(z/2) (51450 z - 25725 z^2 + 4250 z^4 - 2080 z^5 + 552 z^6 + 256 z^7 + 16 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]