A function which is one of the solutions to the Modified Bessel Differential Equation and is closely
related to the Bessel Function of the First Kind . The above plot shows for , 2, ..., 5. In
terms of
,

(1) |

(2) |

(3) |

(4) |

A derivative identity for expressing higher order modified Bessel functions in terms of is

(5) |

**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.

© 1996-9

1999-05-26