The method of comparison equations in the solution of linear second-order differential equations (generalized W.K.B. method)

Springer Science and Business Media LLC - Tập 5 Số 1 - Trang 345-367 - 1956
R. Dingle1
1Department of Physics, University of W. Australia, Nedlands

Tóm tắt

Từ khóa


Tài liệu tham khảo

Applied Mathematics Series (AMS), Dept. of Commerce, National Bureau of Standards, Washington D.C., U.S.A.

British Association Mathematical Tables (BA no), Cambridge Univ. Press.

British Association Reports (BA date).

Conolly, B. W., Quart. J. Mech. Appl. Mach.3 (1950) 236.

Davis, H. T., Tables of the Higher Mathematical Functions, Vol I, Principia Press, Bloomington, Indiana, 1933.

Dinnik, A., Tafeln der Besselschen Funktionen von der gebrochen Ordnung, Allukrainische Akad. Wiss. Naturw-tech Kl. USSR, 1933.

Fletcher, A., J. C. P. Miller, and L. Rosenhead, Index of Mathematical Tables, Scientific Computing Service, London, 1946.

Harvard University Computation Laboratory, Annals 18 & 19, Harvard Univ. Press, Cambridge, U.S.A., 1948-9.

Heuman, C., J. Math. Phys.20 (1941) 127.

Jahnke, E., and F. Emde, Tables of Functions, Dover, N.Y., 1945.

Jeffreys, H., and B. Jeffreys, Methods of Mathematical Physics, 2nd ed., Cambridge Univ. Press, 1950.

Kotani, M., et alia, Proc. Phys-Math. Soc. Japan,20, extra no 1, 1938;22, extra no., 1940.

Langer, R. E., Trans. Amer. Math. Soc.37 (1935) 397; Phys. Rev.51 (1937) 669.

Legendre, A. M., Tables of the Complete and Incomplete Elliptic Integrals, ed. K. Pearson, Biometrika Office, London, 1934.

MacDonald, A. D., J. Math. Phys.28 (1949) 183; Research Lab. of Electronics, M.I.T. Tech. Rep. 130, 1949; Can. J. Res.A28, (1950) 175.

Mursi, Z., Tables of Legendre Associated Functions, Fouad I University, Cairo, 1941.

Pearson, K., Tables of the Incomplete Gamma-Function, Cambridge Univ. Press, Re-issue 1951.

Placzek, G., The FunctionsE n (x), MT-1, National Research Council of Canada, Division of Atomic Energy, 1946.

Russell, J. B., J. Math. Phys.12 (1933) 291.

Sommerfeld, A., Atomic Structure and Spectral Lines, I, Methuen, 3rd ed. 1934.

Watson, G. N., Proc. Roy. Soc.A94 (1918) 190; Theory of Bessel Functions Cambridge Univ. Press, 1922 (2nd ed. 1952).