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The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the $n$th powers of $\pi^2$, $\pi^4$ and $\pi^8$ can be expressed in terms of the $n$th elementary symmetric functions.
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참고문헌 (18)
참고문헌 신청
J. G. F. Belinfante / 1989 / Problems and Solutions: Solutions of Elementary Problems: E3237 / Amer. Math. Monthly 96(4):364~365
B. C. Berndt / 1994 / Ramanujan's notebooks. Part IV / Springer-Verlag
M. Chellali / 1988 / Acceleration de calcul de nombres de Bernoulli / J. Number Theory 28(3):347~362
R. Honsberger / 1985 / Mathematical Gems. III / Mathematical Association of America
F. T. Howard / 1995 / Applications of a recurrence for the Bernoulli numbers / J. Number Theory 52(1):157~172
B. C. Berndt / 1994 / Ramanujan's notebooks. Part IV / Springer-Verlag
M. Chellali / 1988 / Acceleration de calcul de nombres de Bernoulli / J. Number Theory 28(3):347~362
R. Honsberger / 1985 / Mathematical Gems. III / Mathematical Association of America
F. T. Howard / 1995 / Applications of a recurrence for the Bernoulli numbers / J. Number Theory 52(1):157~172
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