Abstract
This chapter discusses Bessel functions and their integrals. In the hypergeometric notation, Bessel functions of the first kind can be expressed in terms of a 0F1 or a 1F1. The analytical material in this chapter is kept to a minimum. The principal emphases are on coefficients for expansions in infinite series of Chebyshev polynomials of the first kind and rational approximations. The chapter presents analytical formulas for the expansion of Bessel functions in series of Chebyshev polynomials of the first kind. A comparison of the results affords some appreciation of the accuracy of the coefficients when compared with those for the expansion in an infinite series of Chebyshev polynomials.
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