- Title
- Empirically determined Apéry-like formulae for ζ(4n+3)
- Creator
- Borwein, Jonathan; Bradley, David
- Relation
- Experimental Mathematics Vol. 6, Issue 3, p. 181-194
- Publisher Link
- http://dx.doi.org/10.1080/10586458.1997.10504608
- Publisher
- A. K. Peters
- Resource Type
- journal article
- Date
- 1997
- Description
- Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for ζ(4n+3) that 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 nontrivial combinatorial identity. The identity is equivalent to an interesting new integral evaluation for the central binomial coefficient. We outline a new technique for transforming and summing certain infinite series. We also derive a formula that provides strange evaluations of a large new class of nonterminating hypergeometric series.
- Subject
- Apéry's series; Apéry-like formulae; formulae; Riemann zeta function
- Identifier
- http://hdl.handle.net/1959.13/940789
- Identifier
- uon:13102
- Identifier
- ISSN:1058-6458
- Language
- eng
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