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On the properties of a special function defined by an integral. (English) Zbl 1124.33022

The properties of a function which is defined by an integral are presented. The numerical of this function are tabulated correct to twenty decimal places. The waves of this function and its complementary are plotted. Some properties of this function are investigated. The value in \(\infty\) is \(\frac{8}{\pi^2} \sum^\infty_{n=1}\frac{1}{(2n-1)^2}\).

MSC:

33E20 Other functions defined by series and integrals
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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