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XIX.—On the Determination of the General Term in Green-type Expansions*

Published online by Cambridge University Press:  14 February 2012

S. Jorna
S. Jorna
Affiliation:
Institute for Radiation Physics and Aerodynamics, University of California, San Diego, La Jolla, California.
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Synopsis

A formal method is developed for deriving a series expansion of the general term in Green-type expansions. The technique is exemplified by detailed calculations for modified Bessel functions of large order.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 4 , 1967 , pp. 243 - 255
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

References to Literature

Airey, J. R., 1937. “Converging Factor” in Asymptotic Series and the Calculation of Bessel, Laguerre and other functions, Phil. Mag., 24, 521–552.CrossRefGoogle Scholar
British Association, 1960. Mathematical Tables, vol. X, Bessel functions (part II). C.U.P.Google Scholar
Davis, H. T., 1935. “Tables of higher mathematical functions”, Vol. II. Principia Press.Google Scholar
Dingle, R. B., 1958. “Asymptotic expansions and converging factors”, Proc. Roy. Soc. A, 244, 456–475, 476–483, 484–490.Google Scholar
Dingle, R. B., 1959. “Asymptotic expansions and converging factors”, Proc. Roy. Soc., A, 249, 270–283, 284–292, 293–296.Google Scholar
Erdelyi, A., Magnus, F., Oberhettinger, F., and Tricomi, F., 1953–55. “Higher transcendental functions”, (3 Vols.). McGraw-Hill, New York.Google Scholar
Jordan, C., 1960. “Calculus of finite differences” (reprint of 2nd edn.). Chelsea Publ. Co., New York.Google Scholar
Jorna, S., 1964. “Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations”, Proc. Roy. Soc. A, 281, 99–110, 111–129.Google Scholar
Jorna, S., 1965. “Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations”, Proc. Roy. Soc. A, 284, 531–539, 286, 366–375.Google Scholar
Miller, J. C. P., 1952. “A method for the determination of converging factors, applied to the asymptotic expansions for the parabolic cylinder functions”, Proc. Camb. Phil. Soc., 48, 243–254.CrossRefGoogle Scholar
Nörlund, N. E., 1954. “Differenzenrechnung”, (reprint of 1923 edn.). Chelsea Publ. Co., New York.Google Scholar
Watson, G. N., 1944. “Theory of Bessel functions”, 2nd edn. C.U.P.Google Scholar