Let p > 5 be a prime. We prove congruences modulo p(3-d) for sums of the general form Sigma((p -3)/2)(k=0) ((2k)(k))t(k)/(2k + 1)(d+1) and Sigma((p-1)/2)(k=1) ((2k)(k))t(k)/kd with d = 0, 1. We also consider the special case t = (-1)(d)/16 of the former sum, where the congruences hold modulo p(5-d).

Pilehrood, K., Pilehrood, T., Tauraso, R. (2012). Congruences concerning Jacobi polynomials and Apery-like formulae. INTERNATIONAL JOURNAL OF NUMBER THEORY, 8(7), 1789-1811 [10.1142/S1793042112501035].

Congruences concerning Jacobi polynomials and Apery-like formulae

TAURASO, ROBERTO
2012-01-01

Abstract

Let p > 5 be a prime. We prove congruences modulo p(3-d) for sums of the general form Sigma((p -3)/2)(k=0) ((2k)(k))t(k)/(2k + 1)(d+1) and Sigma((p-1)/2)(k=1) ((2k)(k))t(k)/kd with d = 0, 1. We also consider the special case t = (-1)(d)/16 of the former sum, where the congruences hold modulo p(5-d).
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Congruence; finite central binomial sum; harmonic sum; Bernoulli number; Euler number; Jacobi polynomials
Pilehrood, K., Pilehrood, T., Tauraso, R. (2012). Congruences concerning Jacobi polynomials and Apery-like formulae. INTERNATIONAL JOURNAL OF NUMBER THEORY, 8(7), 1789-1811 [10.1142/S1793042112501035].
Pilehrood, K; Pilehrood, T; Tauraso, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/90048
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