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New Continued Fraction Expansions and Inequalities for n! into Negative Powers of a Triangular Number

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Abstract

In this paper, based on Stirling’s formula and Gosper’s formula, we establish some new continued fraction expansions and inequalities for n! into negative powers of a triangular number. Finally, to demonstrate the superiority of our new series over classical ones, some numerical computations are given.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, China

    Dawei Lu, Lixin Song & Qinxin Xu

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  1. Dawei Lu
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  2. Lixin Song
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  3. Qinxin Xu
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Correspondence to Lixin Song.

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Lu, D., Song, L. & Xu, Q. New Continued Fraction Expansions and Inequalities for n! into Negative Powers of a Triangular Number. Results Math 72, 765–786 (2017). https://doi.org/10.1007/s00025-017-0701-9

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  • DOI: https://doi.org/10.1007/s00025-017-0701-9

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