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A Short Proof of Krattenthaler Formulas

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Abstract

With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations, called the Krattenthaler forumlas. The present paper presents a very short proof of this formula via Lagrange interpolation. Further, our method of proof declares that the Krattenthaler result is unique in the light of Lagrange interpolation.

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References

  1. Gould H. W., Hsu L. C., Some new inverse series relation, Duke Math. J., 1973, 40:881–891

    Article  Google Scholar 

  2. Carlitz L., Some inverse relations, Duke. Math. J., 1973, 893–901

  3. Bressoud D. M., A matrix inverse, Proc. Amer. Math. Soc., 1983, 88:44–48

    Article  MathSciNet  Google Scholar 

  4. Gessel I., Stanton D., Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc., 1982, 277:173–201

    Article  MathSciNet  Google Scholar 

  5. Krattenthaler C., Operator methods and Lagrange inversion—a unified approach to Lagrange formulas, Trans. Amer. Math. Soc., 1988, 305:431–465

    Article  MATH  MathSciNet  Google Scholar 

  6. Krattenthaler C., A new matrix inverse, Proceeding of American Math. Soc., 1996, 124(1):47–59

    Article  MATH  MathSciNet  Google Scholar 

  7. Andrews G. E., Multiple series Roger-Ramanujan type identities, Pacific J. Math., 1984, 114:267–283

    MATH  MathSciNet  Google Scholar 

  8. Andrews G. E., q-Series: their development and application in analysis, number theory, combinatorics, physics and computer algebra, NSF CBMS Regional Conf. Series, 1986, 66

  9. Chu W. C., Hsu L. C., Some new applications of Gould-Hsu inversion, J. Combine Inform System Sci., 1989, 14:1–4

    MATH  Google Scholar 

  10. Stephen C., Milne, Bhatnagar G., A characterization of inverse relations, Discrete Mathematics, 1998, 193:235–245

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Xin Rong Ma.

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Ma, X.R. A Short Proof of Krattenthaler Formulas. Acta Math Sinica 18, 289–292 (2002). https://doi.org/10.1007/s101140200161

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  • DOI: https://doi.org/10.1007/s101140200161

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