On the numerical solution of a differential-difference equation arising in analytic number theory

Authors:
J. van de Lune and E. Wattel

Journal:
Math. Comp. **23** (1969), 417-421

MSC:
Primary 65.70

DOI:
https://doi.org/10.1090/S0025-5718-1969-0247789-3

MathSciNet review:
0247789

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Abstract: In the January 1962 issue of this Journal R. Bellman and B. Kotkin published a short paper under the same title as this one (cf. [1]). In that paper Bellman and Kotkin presented some of their results concerning the numerical computation of the continuous function , defined by

**[1]**R. Bellman & B. Kotkin, ``On the numerical solution of a differential-difference equation arising in analytic number theory,''*Math. Comp.*, v. 16, 1962, pp. 473-475. MR**26**#5756. MR**0148248 (26:5756)****[2]**N. G. de Brtjijn, ``The asymptotic behaviour of a function occurring in the theory of primes,''*J. Indian Math. Soc.*, v. 15, 1951, pp. 25-32. MR**13**, 326. MR**0043838 (13:326f)****1.**For an extensive list of literature concerning the function we refer to 3. J. van de Lune & E. Wattel,*On the Frequency of Natural Numbers m whose Prime Divisors are all Smaller than*, Mathematical Centre, Amsterdam, Report ZW 1968-007, 1968.

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0247789-3

Article copyright:
© Copyright 1969
American Mathematical Society