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Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the paper, the authors find integral representations, complete monotonicity, limits, and other properties of remainders of the Binet and Stirling formulas for the gamma function and their derivatives. These properties strengthen almost all results in three papers published in the Journal of Computational and Applied Mathematics, Applied Mathematics Letters, and Applied Mathematics and Computation in the years 2006, 2011, and 2014 by seven mathematicians. The proofs in the paper unify and are simpler than those in the three papers.

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Acknowledgments

The authors thank Dr. Songbai Guo in China and Professor Cristinel Mortici in Romania for their helpfully commenting on, carefully correcting to, and patiently checking up the original version of this paper.

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Authors and Affiliations

  1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China

    Feng Qi

  2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, 028043, Inner Mongolia, China

    Feng Qi

  3. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300387, China

    Feng Qi

  4. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China

    Bai-Ni Guo

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  1. Feng Qi
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Correspondence to Feng Qi.

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Qi, F., Guo, BN. Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function. RACSAM 111, 425–434 (2017). https://doi.org/10.1007/s13398-016-0302-6

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  • DOI: https://doi.org/10.1007/s13398-016-0302-6

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