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Summations of Schlömilch series containing Struve function terms

  • Dragana Jankov Maširević EMAIL logo
Published/Copyright: May 12, 2016
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Abstract

In this note we present a new proof of certain closed expressions derived by Lorch and Szego [5] for the Schlömilch series containing Struve functions 𝐇ν and show their validity for an essentially wider range of variables when ν>-12.

Acknowledgements

The author wishes to thank Tibor K. Pogány for his very kind and continuous help in preparing, improving and finishing the manuscript.

References

[1] Abramowitz M. and Stegun I. A., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, National Bureau Stand. Appl. Math. Ser. 55, U.S. Government Printing Office, Washington, 1965. 10.1115/1.3625776Search in Google Scholar

[2] Cvijović D., New integral representations of the polylogarithm function, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2007), no. 2080, 897–905. 10.1098/rspa.2006.1794Search in Google Scholar

[3] Erdélyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher Transcendental Functions, Vol. I, McGraw–Hill, New York, 1955. Search in Google Scholar

[4] Gradshteyn I. S. and Ryzhik I. M., Table of Integrals, Series, and Products, 4th ed., Academic Press, New York, 1965. Search in Google Scholar

[5] Lorch L. and Szego P., Closed expressions for some infinite series of Bessel and Struve functions, J. Math. Anal. Appl. 122 (1987), no. 1, 47–57. 10.1016/0022-247X(87)90343-XSearch in Google Scholar

[6] Miller A. R., On the Mellin transform of products of Bessel and generalized hypergeometric functions, J. Comput. Appl. Math. 85 (1997), no. 2, 271–286. 10.1016/S0377-0427(97)00129-5Search in Google Scholar

Received: 2014-10-20
Accepted: 2015-3-26
Published Online: 2016-5-12
Published in Print: 2016-9-1

© 2016 by De Gruyter

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