Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)
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چکیده
منابع مشابه
Empirically Determined Apéry-Like Formulae for ζ(4n+3)
Research supported by NSERC, the Natural Sciences and Engineering Research Council of Canada. Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for (4n+3) that generalizes Apéry’s series for (3), and appears to give the best possible series relations of this type, at least for n< 12. The formula reduces to a finit...
متن کامل6 Experimental Determination of Apéry - Like Identities for ζ ( 2 n + 2 )
We document the discovery of two generating functions for ζ(2n + 2), analogous to earlier work for ζ(2n + 1) and ζ(4n + 3), initiated by Koecher and pursued further by Borwein, Bradley and others.
متن کاملExperimental Determination of Apéry-like Identities for ς(2n + 2)
We document the discovery of two generating functions for ζ(2n + 2), analogous to earlier work for ζ(2n + 1) and ζ(4n + 3), initiated by Koecher and pursued further by Borwein, Bradley and others.
متن کاملM ay 2 00 5 Empirically Determined Apéry - Like Formulae for ζ ( 4 n + 3 )
Abstract. Some rapidly convergent formulae for special values of the Riemann Zeta function are given. We obtain a generating function formula for ζ(4n+3) which generalizes Apéry’s series for ζ(3), and appears to give the best possible series relations of this type, at least for n < 12. The formula reduces to a finite but apparently non-trivial combinatorial identity. The identity is equivalent ...
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was first obtained by A. Markov in 1890, but became more widely known after its appearance in connection with Apéry’s proof of the irrationality of ζ(3). We outline here the role that hypergeometric functions play in generating more general series acceleration formulae for values of the Riemann zeta function at the positive integers. At odd positive integers, we have the formulae of Koecher, an...
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 8 شماره
صفحات -
تاریخ انتشار 1999