Showing papers on "Cylindrical harmonics published in 1975"

New applications of Poisson's summation formula

Abstract: Fourier expansions in modified Bessel functions are evaluated in terms of elementary functions. The results are obtained in the form of rapidly convergent series so that numerical computations are quite easy. This leads to the possibility of tabulating the modified Bessel functions in their critical domain. A physical application is also given: simple expansions giving the Madelung constant for cubic crystallographic structures are established; they involve only elementary functions and exhibit the greatest known accuracy.

Remark on “Algorithm 236: Bessel Functions of the First Kind [S17]”

Abstract: The procedures in Algorithm 236 were coded in PL / I and run on the IBM 370/165. The following error was discovered for a = O, nmax large, and x small, e.g. nmax = 50 and x = 0.5. In the last if statement in three of the procedures, Japlusn, Iaplusn, and Complex Japlusn, division by zero took place. Not all compilers and computers would pose problems for the above values of the parameters; whether or not they do depends on the permissible magnitude of the flouting-point numbers for the compiler and computer used. For the IBM 370/165 the smallest positive floating-point number which the computer can hold is approximately 5.40 X 10 -79 (see [10, p. 163]). The following corrections should be made in the procedure Japlusn. The last if statement should be replaced by