• Corpus ID: 5384788

Hypergeometric-like Representation of the Zeta-Function of Riemann

@article{Malanka2001HypergeometriclikeRO,
  title={Hypergeometric-like Representation of the Zeta-Function of Riemann},
  author={Krzysztof D. Maślanka},
  journal={arXiv: Mathematical Physics},
  year={2001}
}
  • K. Maślanka
  • Published 4 May 2001
  • Mathematics
  • arXiv: Mathematical Physics
We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within the theory of the zeta-function of Hawking offering thus a variety of applications in quantum field theory, quantum cosmology and statistical mechanics. 

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References

SHOWING 1-2 OF 2 REFERENCES

Hypergeometric-like Representation of the Zeta-Function of Riemann, Cracow Observatory preprint, 1997; cf. also: AMS preprints http://www.ams.org/preprints

  • Hypergeometric-like Representation of the Zeta-Function of Riemann, Cracow Observatory preprint, 1997; cf. also: AMS preprints http://www.ams.org/preprints
  • 1997

Comm. Math. Phys

  • Comm. Math. Phys
  • 1977