Roots of two transcendental equations as functions of a continuous real parameter
Robert L. Pexton and Arno D. Steiger
Math. Comp. 32 (1978), 511-518
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Abstract: The roots, and , of the transcendental equations and where are considered as functions of the continuous real parameter . The symbols and denote the spherical Bessel functions of the first and second kind. The two transcendental equations are invariant under the transformations and , respectively. Therefore, only positive roots are discussed. All the -roots increase monotonically as increases in the open interval (0, 1). For each order l, the smallest -root decreases monotonically as increases in (0, 1), tending towards as approaches unity. For all the other -roots have a minimum value equal to .
L. Pexton and Arno
D. Steiger, Roots of two transcendental equations
involving spherical Bessel functions, Math.
Comp. 31 (1977), no. 139, 752–753. MR 0438662
(55 #11570), http://dx.doi.org/10.1090/S0025-5718-1977-0438662-0
M. ABRAMOWITZ & I. A. STEGUN, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series No. 55, U. S. Government Printing Office, Washington, D. C., 1965.
- ROBERT L. PEXTON & ARNO D. STEIGER, "Roots of two transcendental equations involving spherical Bessel functions," Math. Comp., v. 31, 1977, pp. 752-753. MR 0438662 (55:11570)
- M. ABRAMOWITZ & I. A. STEGUN, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series No. 55, U. S. Government Printing Office, Washington, D. C., 1965.
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