Common zeros of two Bessel functions. II. Approximations and tables

Author:
T. C. Benton

Journal:
Math. Comp. **41** (1983), 203-217

MSC:
Primary 33A40; Secondary 65A05

DOI:
https://doi.org/10.1090/S0025-5718-1983-0701635-7

MathSciNet review:
701635

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Abstract: In [1] it was shown that two Bessel functions , could have two zeros which were common to both functions, and a computer program was made which takes approximate values of , and and and from them computes the exact values. Here it will be shown how to find the necessary approximate values to initiate the computation. A table of the smaller ratios *m* : *n* with the orders of the functions less than one hundred is given.

**[1]**T. C. Benton & H. D. Knoble, "Common zeros of two Bessel functions,"*Math. Comp.*, v. 32, 1978, pp. 533-535. MR**0481160 (58:1303)****[2]**G. N. Watson,*Treatise on Bessel Functions*, Cambridge Univ. Press, Oxford, 1945.**[3]**Royal Society Mathematical Tables 7.*Bessel Functions*III (F. W. T. Olver, ed.), Cambridge Univ. Press, Oxford, 1960.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0701635-7

Article copyright:
© Copyright 1983
American Mathematical Society