Showing papers on "Inverse trigonometric functions published in 1968"

Inverse Functions of the Products of Two Bessel Functions and Applications to Potential Scattering

Abstract: Inverse functions of products of two Bessel functions jl(xy)jm(xy) are determined for the cases m = l, l + 1, and l + 2. Integral representations for these inverse functions in terms of Neumann functions are given, and some of the simplest ones are expressed in terms of trigonometric functions.We show how one may obtain an integral representation for any well‐behaved function in terms of products of two Bessel functions, with the help of these inverse functions and also outline some of their applications to potential scattering. In particular, we demonstrate the usefulness of the inverse functions in determining the potential explicitly from the phase shifts in the Born approximation.

Note on a pair of dual trigonometric series

Abstract: It is the purpose of this note to discuss the solution of the pair of serieswhere F(x) and G(x) are given and the coefficients an are to be determined.

Inverse tangent generator

Abstract: Apparatus for generating the inverse tangent function from 0* to 360* to any desired degree of accuracy includes means for mechanizing equations involving the ratios of arithmetic quantities having relatively few terms. Resistance networks may be employed; and two variable elements yield an accuracy of nearly 0.001 second of arc, while three variable elements yield an accuracy better than 2 X 10 9 second of arc. Time-sharing permits these accuracies to be obtained with only one variable element. The tangent function may also be generated with corresponding accuracy within a region extending from 0* to somewhat less than 90*.