| 释义 |
Modified Bessel Function of the First KindA function  which is one of the solutions to the Modified Bessel Differential Equation and is closelyrelated to the Bessel Function of the First Kind  . The above plot shows for  , 2, ..., 5. Interms of,
 | (1) |
 , the function can be computed using
 | (2) |
 is the Gamma Function. An integral formula is
 | (3) |
 to
 | (4) |
A derivative identity for expressing higher order modified Bessel functions in terms of  is
 | (5) |
 is a Chebyshev Polynomial of the First Kind. See also Bessel Function of the First Kind, Modified Bessel Function of the First Kind, Weber's Formula
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Modified Bessel Functions  and  .'' §9.6 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 374-377, 1972.Arfken, G. ``Modified Bessel Functions,  and  .'' §11.5 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 610-616, 1985. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/cntfrc/cntfrc.html Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions.'' §6.7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 234-245, 1992. Spanier, J. and Oldham, K. B. ``The Hyperbolic Bessel Functions and  '' and ``The General Hyperbolic Bessel Function .'' Chs. 49-50 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 479-487 and 489-497, 1987.
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