On the use of asymptotic approximations of Green's type when the coefficient has zeros
- 1 January 1956
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 52 (1) , 61-66
- https://doi.org/10.1017/s030500410003098x
Abstract
Allowance is made for the error terms in the cases where χ has a simple zero at x = 0, or two simple zeros at a; = ± 1 (with χ either positive or negative for − 1 < x < 1). The errors of the approximations given by neglecting the error terms are found to be small in all cases, sometimes much smaller than there was any previous reason to expect.Keywords
This publication has 5 references indexed in Scilit:
- Methods of Mathematical PhysicsPhysics Today, 1956
- On approximate solutions of linear differential equationsMathematical Proceedings of the Cambridge Philosophical Society, 1953
- Note on the transparency of a potential barrierMathematical Proceedings of the Cambridge Philosophical Society, 1942
- The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to the Stokes phenomenonBulletin of the American Mathematical Society, 1934
- On Certain Solutions of Mathieu's EquationProceedings of the London Mathematical Society, 1925