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Some identities of Bernoulli and Euler polynomials arising form umbral calculus
김대산,김태균 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1
In this paper, we give some interesting identities of Bernoulli and Euler polynomials which are derived from umbral calculus.
Sheffer sequences for the powers of Sheffer pairs under umbral composition
김대산,T. Kim,C. S. Ryoo 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In this paper we study some properties of Sheffer sequences for the powers of Sheffer pairs under umbral composition.
Symmetry identities for generalized twisted Euler polynomials twisted by unramified roots of unity
김대산 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.3
We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Euler polynomials and alternating generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure similar to that introduced by Koblitz, of the generating function for the generalized twisted Euler polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the alternating generalized twisted power sums.
A note on q-Eulerian polynomials
김대산,김태균 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.4
In this paper, we consider a new construction of the q-extension of Eulerian polynomials which are different from Carlits's q-Eulerian polynomials
ON THE ASSOCIATED SEQUENCE OF SPECIAL POLYNOMIALS
김대산,김태균,이승훈,임석훈 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.
Abundant symmetry for higher-order Bernoulli polynomials (II)
김대산,이나리,JIYOUNG NA,박경호 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3
We derive twenty five basic identities of symmetry in three vari-ables related to higher-order Bernoulli polynomials and power sums. Thisdemonstrates that there are abundant identities of symmetry in the threevariable case, in contrast to the two variable case, where there are only a few. These are new, since there have been results only about identities of symmetryin two variables. The derivations of identities are based on the p-adic integralexpression of the generating function for the higher-order Bernoulli polyno-mials and the quotient of integrals that can be expressed as the exponentialgenerating function for the power sums.
Codes associated with O(3,2^r) and power moments of Kloosterman sums with trace one arguments
김대산 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.2
We construct a binary linear code C(O(3; q)), associated with the orthogonal group O(3; q). Here q is a power of two. Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes C(O(3; q)) and C(Sp(2; q)). This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.
Some arithmetic properties of Bernoulli and Euler numbers
김대산,T. Kim,김영희,S. H. LEE 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.4
In this paper, we give some arithmatic identities for the Bernoulli and the Euler numbers. These identities are derived from the several p-adic integral equations on Z_p.
Barnes-type degenerate Bernoulli polynomials
김대산,T. Kim,D. V. Dolgy,T KOMATSU 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.1
In this paper, for any positive integer r, we consider the Barnes-type degenerate Bernoulli polynomials βn(λ, x|a1,...,ar) (a1,...,ar ≠ 0), generalizing the degener- ate Bernoulli polynomials βn(λ, x) (λ ≠ 0). From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.
FROBENIUS-TYPE EULERIAN POLYNOMIALS AND UMBRAL CALCULUS
김대산,김태균,임석훈 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.2
In this paper, we define and study some properties of FrobeniustypeEulerian polynomials arising from umbral calculus. From our resultsfor the properties of Frobenius-type Eulerian polynomials, we derivemany interesting identities about Frobenius-type Eulerian polynomials.