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Summation formulas of q-series by modified Abel's lemma

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By means of Abel's lemma on summation by parts, we revisit several basic hypergeometric series identities. Furthermore, some new summation formulas are also established.

Abstract

By means of Abel's lemma on summation by parts, we revisit several basic hypergeometric series identities. Furthermore, some new summation formulas are also established.

참고문헌 (12)

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  6. Adiga, C., "On a q-analogue of S andor's funtion", JIPAM. J. Inequal. Pure Appl. Math, 4(5), pp.5~ (2003)
  7. G. Gasper, "Basic Hypergeometric Series" (2004), Cambridge University Press
  8. Kim, Taekyun, "Sums of powers of consecutive q-integers", Adv. Stud. Contemp. Math, 9(1), pp.15~18 (2004)
  9. Kim, T, "q-Bernoulli numbers and polynomials associated with Gaussian binomial coe±-cients", Russ. J. Math. Phys, 15(1), pp.51~57 (2008)
  10. Kim, T., "q-extension of the Euler formula and trigonometric functions", Russ. J. Math. Phys, 14(3), pp.275~278 (2007)
  11. Kim, Taekyun, "On the q-analogue of gamma functions and related inequalities", JIPAM. J. Inequal. Pure Appl. Math, 6(4), pp.4~ (2005)
  12. Taekyun Kim, "The modified q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 16(2), pp.161~170 (2008), 장전수학회(章田數學會)

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