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  • Dixit, Atul; Glasser, M. Lawrence; Moll, Victor H.; Vignat, Christophe (Springer, 2016-12)
    In 1998 Don Zagier introduced the modified Bernoulli numbers B∗n and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of B∗2n, and also ...
  • Dixit, Atul; Glasser, M. Lawrence; Moll, Victor H.; Vignat, Christophe (SpringerOpen, 2017-07)
    In 1998 Don Zagier introduced the modified Bernoulli numbers B∗nBn∗ and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of B∗2nB2n∗, and ...
  • Dixit, Atul; Kesarwani, Aashita; Moll, Victor H. (Elsevier, 2017-10)
    A new generalization of the modified Bessel function of the second kind is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby ...
  • Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru (Elsevier, 2018-11)
    Letrk(n) denote the number of representations of the positive integernas thesum ofksquares. We rigorously prove for the first time a Vorono ?? summation formula forrk(n), k?2,proved incorrectly by A. I. Popov and later ...

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