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Calculate modified Bessel function of the first kind and order 0

        i0kappa #

Description

    i0kappa calculates individual values of I_0(), the modified Bessel
    function of the first kind and order 0, so long as the argument is at
    least -3.75. Polynomial approximations are used for the separate cases in
    which the argument is more than or not more than 3.75. See Abramowitz and
    Stegun (1965), in particular formulae (9.8.1) and (9.8.2) on p.378.


Remarks

    Usually this program will be used within other programs. For general
    background on this and related functions, see texts such as Andrews,
    Askey and Roy (1999).  The particular problem motivating this program was
    supporting calculations for the von Mises distribution in circular
    statistics, on which see for example Fisher (1993).


Examples

    . i0kappa 5


Author 

    Nicholas J. Cox, University of Durham, U.K.
    n.j.cox@durham.ac.uk


References

    Abramowitz, M. and Stegun, I.A. (eds) 1965.  Handbook of mathematical
        functions. New York: Dover.

    Andrews, G.E., Askey, R. and Roy, R. 1999. Special functions.  Cambridge:
        Cambridge University Press.

    Fisher, N.I. 1993. Statistical analysis of circular data.  Cambridge:
        Cambridge University Press.