# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
(2) For b = 1, c = -1, we obtain the modified Bessel functions of first kind of order v whose series form is given as
[J.sub.m] and [Y.sub.m] are the Bessel functions of the first and second kinds and [I.sub.m] and [K.sub.m] are modified Bessel functions of the first and second kinds, respectively.
where the argument of the modified Bessel functions [I.sub.v](*) and [K.sub.v] (*) is j[k.sub.1][rho]/2, and
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. A shorter version covers only ordinary differential equations, for a one-semester or one-quarter course.
where G(r, r') is the Green function of (3.10), which involves the modified Bessel functions [I.sub.1]([square root of [[beta].sub.n]] r) and [K.sub.1]([square root of [[beta].sub.n]] r).
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
This relation is similar to the relation between Bessel and modified Bessel functions.
where [mu] = ([lambda.sub.uo] [lambda.sub.ou][t.sub.u][t.sub.o])[sup.1/2], and [I.sub.o] (.) and .[I.sub.1] (.) are modified Bessel functions of the first kind of order zero and one, respectively.
To obtain a solution of Equation 1 involves calculating Bessel functions and modified Bessel functions. Methods that use numerical techniques to solve these functions on calculators or on desktop computers have involved the use of an algorithm that detracts from the accuracy.
where the argument of the modified Bessel functions has been omitted for notational simplicity.

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