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In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as ap- plications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.
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참고문헌 (26)
참고문헌 신청
A. Bazs´o / 2012 / A refinement of Faulhaber’s theorem con-cerning sums of powers of natural numbers / Appl. Math. Lett 25 (3) : 486 ~ 489
A. Erd´elyi / 1953 / Higher Transcendental Functions. Vol 1 / McGraw Hill
B. C. Berndt / 1989 / Ramanujan’s Notebooks. Part II / Springer-Verlag
B. Cho / 2013 / Evaluation of a certain combinatorial convolution sum in higher level cases / J. Math. Anal. Appl 406 (1) : 203 ~ 210
D. B. Lahiri / 1946 / On Ramanujan’s function τ(n) and the divisor function σ(n). I / Bull. Calcutta Math. Soc 38 : 193 ~ 206
A. Erd´elyi / 1953 / Higher Transcendental Functions. Vol 1 / McGraw Hill
B. C. Berndt / 1989 / Ramanujan’s Notebooks. Part II / Springer-Verlag
B. Cho / 2013 / Evaluation of a certain combinatorial convolution sum in higher level cases / J. Math. Anal. Appl 406 (1) : 203 ~ 210
D. B. Lahiri / 1946 / On Ramanujan’s function τ(n) and the divisor function σ(n). I / Bull. Calcutta Math. Soc 38 : 193 ~ 206
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