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A note on the Moll–Arias de Reyna integral

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Abstract

The Moll–Arias de Reyna integral

$$\begin{aligned} \int _0^{\infty }\frac{\mathrm{d}x}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi (x)+\sqrt{\varphi (x)}}} \quad \text { where } \varphi (x)=1+\frac{4}{3}\left( \frac{x}{x^2+1}\right) ^2 \end{aligned}$$

is generalized and several values are given.

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References

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Acknowledgements

The author thanks Victor Moll for informing him of [2, 3].

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Authors and Affiliations

  1. Departamento de Física Teórica, Atómica y Óptica, Facultad de Ciencias, University of Valladolid, Valladolid, 40007, Spain

    M. L. Glasser

  2. Department of Physics, Clarkson University, Potsdam, NY, 13676, USA

    M. L. Glasser

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  1. M. L. Glasser
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Correspondence to M. L. Glasser.

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Partial financial support is acknowledged to the Spanish Junta de Castilla y León (VA057U16) and MINECO (Project MTM2014-57129-C2-1-P).

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Glasser, M.L. A note on the Moll–Arias de Reyna integral. Ramanujan J 51, 329–332 (2020). https://doi.org/10.1007/s11139-018-0091-y

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  • DOI: https://doi.org/10.1007/s11139-018-0091-y

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