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XXIII.—Zeros and Turning Points of the Elliptic-cylinder Functions

Published online by Cambridge University Press:  15 September 2014

E. L. Ince
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Extract

In any discussion of the zeros and turning points of the elliptic-cylinder function it is not necessary to define them more precisely than as functions of period π or 2π which satisfy the Mathieu equation

for the corresponding characteristic values of a. To simplify the following discussion, it is convenient merely to impose the condition that y(0)>0 if y(x) is even, and y′(0)>0 if y(x) is odd.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 52 , 1933 , pp. 424 - 433
Copyright
Copyright © Royal Society of Edinburgh 1933

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References

page 424 note * Ince, , Journ. London Math. Soc., ii, 1927, 47.Google Scholar

page 424 note † Confirmation of this fact is given in § 5.

page 426 note * Cf. Goldstein, , Proc. London Math. Soc., (2) xxviii, 1928, 94.Google Scholar

page 426 note † Ince, , Proc. Roy. Soc. Edin., xlvi, 1926, 318.Google Scholar

page 426 note ‡ Ince, loc. cit.

page 427 note * Proc. Roy. Soc. Edin., xlix, 1929, 215.

page 428 note * Whittaker, and Watson, , Modern Analysis, § 19.61.Google Scholar