Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4710)

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=7/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=7/2, b₁=1/2

http://functions.wolfram.com/07.25.03.4710.01

Input Form

HypergeometricPFQ[{-(9/2), 7/2}, {1/2, 6}, z] == -((1/(43648605 z^3)) (32 E^(z/2) (476280 + 138915 z - 37800 z^2 - 1379700 z^3 + 7885080 z^4 - 8312784 z^5 + 2860608 z^6 - 360960 z^7 + 14336 z^8) BesselI[0, z/2])) + (1/(43648605 z^4)) (32 E^(z/2) (1905120 + 555660 z - 91665 z^2 - 45360 z^3 + 162540 z^4 + 2893224 z^5 - 5950608 z^6 + 2521152 z^7 - 346624 z^8 + 14336 z^9) 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]