Received 2 September, 1947; read 16 October, 1947.
Introduction
Let f(z) be an integral function whose maximum modulus satisfies
|
___ lim r→∞ |
|
≤ 1, |
and such that f(z) and all its derivatives have each at least one zero on or within the circle |z| = ρ. THe Whittaker constant W is the lower bound of these numbers ρ for which at least one such f(z) exists not identically zero. Whittaker and Boas use equivalent definitions. Levinson and Boas proved that
0.7199 < W < 0.7399,
while Pondiczery conjectured that W = 2e–1 = 0.7357.... In this note I show that W < 0.7378, thus reducing the length of the interval in which W is known to lie by about 10 per cent.