modified Bessel functions

modified Bessel functions

[′mäd·ə‚fīd ′bes·əl ‚fəŋk·shənz]
(mathematics)
The functions defined by Iv (x) = exp (-iv π/2) Jv (ix), where Jv is the Bessel function of order v, and x is real and positive. Also known as modified Bessel function of the first kind.
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This edition, revised from the 2009 seventh, includes eight new projects, updated exercise sets, additional examples and figures, a simplified account of linear first-order differential equations, new sections on Green's function and the review of power series, and several boundary-value problems involving modified Bessel functions.
10), which involves the modified Bessel functions [I.
v](z)} are Bessel and modified Bessel functions of order v.
1] is the modified Bessel function of the first order.
This edition has a new section on Green's functions for linear ordinary differential equations; expanded information on modified Bessel functions and problems in cylindrical coordinates; rewritten sections on dot and cross products and independence of path; new problems; and nine new projects.
Since the modified Bessel functions are exponentially suppressed at infinity, the only contribution comes from the lower limit
For a particle moving rapidly compared to thermal speeds we may use the familiar small argument forms for the modified Bessel functions.
N x x > 0 K and 0 I are the modified Bessel functions of zero order with a complex argument.
m,m+1] are again functions of the modified Bessel functions of the first and zero order.
Appendixes cover topics that are not standard parts of an average science of engineering undergraduate curriculum: Green's functions, real spherical harmonics, spherical modified Bessel functions, plane groups and invariant functions, and elementary elasticity theory.
Chebyshev polynomials, modified Bessel functions, Lanczos Tau method, Kontorovich-Lebedev integral transforms
1/2 + i[beta]](x) are related to the modified Bessel functions of the first kind [I.

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