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Apéry sequences and legendre transforms

Published online by Cambridge University Press:  09 April 2009

Yuan Jin
Affiliation:
Department of Mathematics Northwest University710069 Xi'an Shaanxi Province P. R.China e-mail: yuanj@nwu.edu.cn
H. Dickinson
Affiliation:
Department of Mathematics University of York Heslington YorkYO10 5DDEngland e-mail: hd3@york.ac.uk
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Abstract

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A lower bound for the minimal length of the polynomial recurrence of a binomial sum is obtained.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Askey, R. and Wilson, J. A., ‘A recurrence relation generalizing those of Apéry’, J. Austral. Math. Soc. (Series A) 36 (1984), 267278.CrossRefGoogle Scholar
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[3]Franel, J., ‘On a question of J. Franel’, L'intermédiaire des mathématiciens 2 (1895), 3335.Google Scholar
[4]Perlstadt, M. A., ‘Some recurrences for sums of powers of binomial coefficients’, J. Number Theory 27 (1987), No. 3, 304309.CrossRefGoogle Scholar
[5]Schmidt, A. L., ‘Legendre transforms and Apéry's sequences’, J. Austral. Math. Soc. (Series A) 58 (1995), no. 3, 358375.CrossRefGoogle Scholar
[6]Schmidt, A. L. and Yuan, Jin, ‘On recurrences for sums of powers of binomial coefficients’, Technical Report, 1995.Google Scholar
[7]Strehl, V., ‘Binomial identities—combinatorial and algorithmic aspects. Trends in discrete mathematics’, Discrete Math. 136 (1994), no. 1–3, 309346.CrossRefGoogle Scholar
[8]Van der Poorten, A. J., ‘A proof that Euler missed … Apéry's proof of the irrationality of ζ(3). An informal report’, Math Intelligencer 1 (1978/1979), no. 4, 195203.CrossRefGoogle Scholar
[9]Wilf, H. and Zeilberger, D., ‘An algorithmic proof theory for hypergeometric (ordinary and ‘q’) multisum/integral identities’, Invent. Math. 108 (1992), 575633.CrossRefGoogle Scholar
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