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An elliptic integral identity


Author: M. L. Glasser
Journal: Math. Comp. 25 (1971), 533-534
DOI: https://doi.org/10.1090/S0025-5718-71-99715-8
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Abstract | References | Additional Information

Abstract: The definite integral

$\displaystyle {\int_0^\infty {\left[ {\frac{{{{({x^2} + {a^2})}^{1/2}} - a}}{{{... ...^2} + {b^2})}^{1/2}} + b}}} \right]\frac{{dx}}{{{{({x^2} + {b^2})}^{1/2}} + b}}$

is evaluated in closed form.

References [Enhancements On Off] (What's this?)

  • [1] A. Erdélyi et al., Tables of Integral Transforms. Vol. I, McGraw-Hill, New York, 1954, p. 72, Equation (4). MR 15, 868. MR 0061695 (15:868a)
  • [2] M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964, p. 337. MR 29 #4914. MR 0167642 (29:4914)
  • [3] A. Erdélyi et al., Tables of Integral Transforms. Vol. II, McGraw-Hill, New York, 1954, p. 45, Equation (6). MR 16, 168. MR 0065685 (16:468c)
  • [4] W. N. Bailey, J. London ath. Soc., v. 11, 1936, p. 16.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-71-99715-8
Keywords: Definite integral, complete elliptic integral
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society