We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
A lower bound for the minimal length of the polynomial recurrence of a binomial sum is obtained.
[1]Askey, R. and Wilson, J. A., ‘A recurrence relation generalizing those of Apéry’, J. Austral. Math. Soc.(Series A)36 (1984), 267–278.CrossRefGoogle Scholar
[2]
[2]Franel, J., ‘On a question of Laisant’, L'intermédiaire des mathématiciens1 (1894), No. 3, 45–47.Google Scholar
[3]
[3]Franel, J., ‘On a question of J. Franel’, L'intermédiaire des mathématiciens2 (1895), 33–35.Google Scholar
[4]
[4]Perlstadt, M. A., ‘Some recurrences for sums of powers of binomial coefficients’, J. Number Theory27 (1987), No. 3, 304–309.CrossRefGoogle Scholar
[5]
[5]Schmidt, A. L., ‘Legendre transforms and Apéry's sequences’, J. Austral. Math. Soc.(Series A)58 (1995), no. 3, 358–375.CrossRefGoogle Scholar
[6]
[6]Schmidt, A. L. and Yuan, Jin, ‘On recurrences for sums of powers of binomial coefficients’, Technical Report, 1995.Google Scholar
[7]
[7]Strehl, V., ‘Binomial identities—combinatorial and algorithmic aspects. Trends in discrete mathematics’, Discrete Math.136 (1994), no. 1–3, 309–346.CrossRefGoogle Scholar
[8]
[8]Van der Poorten, A. J., ‘A proof that Euler missed … Apéry's proof of the irrationality of ζ(3). An informal report’, Math Intelligencer1 (1978/1979), no. 4, 195–203.CrossRefGoogle Scholar
[9]
[9]Wilf, H. and Zeilberger, D., ‘An algorithmic proof theory for hypergeometric (ordinary and ‘q’) multisum/integral identities’, Invent. Math.108 (1992), 575–633.CrossRefGoogle Scholar