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Mathematics of Computation

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An elliptic integral identity

Author: M. L. Glasser
Journal: Math. Comp. 25 (1971), 533-534
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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.

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Keywords: Definite integral, complete elliptic integral
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society