A note on the arithmetic nature of some infinite series
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Weatherby  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 phrasestranscendental number infinite series Nesterenko’s theorem linear independence
Mathematics Subject Classification11J81 11J72
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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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