# A note on the arithmetic nature of some infinite series

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## Abstract

Weatherby [14] studied some infinite series and proved that they are either zero or transcendental. Here, we extend his results. Moreover, we find a linear independence criteria of these series under some mild conditions.

## Key words and phrases

transcendental number infinite series Nesterenko’s theorem linear independence## Mathematics Subject Classification

11J81 11J72## Preview

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## Notes

### Acknowledgements

I am grateful to the anonymous referee for useful and helpful remarks and comments which improved the presentation of the manuscript. I am thankful to my Ph.D. advisor Professor R. Thangadurai for carefully going through the paper. The part of the work was done during my stay at Harish -Chandra Research Institute, Allahabad, India.

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© Akadémiai Kiadó, Budapest, Hungary 2019