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NOTES ON FORMAL MANIPULATIONS OF DOUBLE SERIES

  • Choi, June-Sang (Department of Mathematics College of Natural Sciences Dongguk University)
  • Published : 2003.10.01
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Abstract

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.

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References

  1. Proc. Edinburgh Math. Soc. v.38 Explicit evaluation of Euler sums D.Borwein;J.M.Borwein;R.Girgensohn https://doi.org/10.1017/S0013091500019088
  2. Pusan-Kyongnam Math. J. v.11 Formal manipulations of double series and their applications J.Choi;T.Y.Seo
  3. Indian J. pure appl. Math. v.27 Explicit formulas for Bernoulli polynomials of order n J.Choi
  4. Die Gammafunktion N.Nielsen
  5. Special Functions E.D.Rainville
  6. An Introduction to the Operations with Series(2nd ed.) I.J.Schwatt
  7. Trans. Amer. Math. Soc. v.347 Remarks on some integrals and series involving the Stirling numbers and ξ(η) Li-Chien Shen https://doi.org/10.2307/2154819
  8. Series Associated with the Zeta and Related Functions H.M.Srivastava;J.Choi

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