An elliptic integral identity
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- by M. L. Glasser PDF
- Math. Comp. 25 (1971), 533-534 Request permission
Abstract:
The definite integral \[ {\int _0^\infty {\left [ {\frac {{{{({x^2} + {a^2})}^{1/2}} - a}}{{{x^2} + {a^2}}}} \right ]} ^{1/2}}K\left [ {\frac {{{{({x^2} + {b^2})}^{1/2}} - b}}{{{{({x^2} + {b^2})}^{1/2}} + b}}} \right ]\frac {{dx}}{{{{({x^2} + {b^2})}^{1/2}} + b}}\] is evaluated in closed form.References
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR 0061695
- Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. II, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR 0065685 W. N. Bailey, J. London ath. Soc., v. 11, 1936, p. 16.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 533-534
- DOI: https://doi.org/10.1090/S0025-5718-71-99715-8