| 释义 |
Modified Bessel Function of the Second KindThe function  which is one of the solutions to the Modified Bessel Differential Equation. The above plotshows for  , 2, ..., 5. is closely related to the Modified Bessel Function of the FirstKind  and Hankel Function  ,
(Watson 1966, p. 185). A sum formula for  is | |  | (4) |
where  is the Digamma Function (Abramowitz and Stegun 1972). An integral formula is
 | (5) |
 , simplifies to
 | (6) |
 | (7) |
 and
The modified Bessel function of the second kind is sometimes called the Basset Function.
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. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Modified Bessel Functions of Integral Order'' and ``Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions.'' §6.6 and 6.7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 229-245, 1992. Spanier, J. and Oldham, K. B. ``The Basset .'' Ch. 51 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 499-507, 1987. Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.
|
