Generalized binomial convolution of the mth powers of the consecutive integers with the general Fibonacci sequence

• Autorzy: Kılıç E. , Akkus I. , Ömür N. , Ulutaş Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.

Słowa kluczowe

EN

binomial convolution; general Fibonacci sequence; Stirling numbers of the second kind

PL

splot dwumianowy; ciąg Fibonacciego; liczby Stirlinga drugiego rodzaju

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 4
• Strony: 379--385
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kılıç E.

• TOBB Economics and Technology University, Mathematics Department, 06560 Ankara, Turkey

autor

Akkus I.

• Kirikkale University, Faculty of Arts and Science, Department of Mathematics, 71450 Kirikkale, Turkey

autor

Ömür N.

• Kocaeli University, Mathematics Department, 41380 Izmit, Turkey

autor

Ulutaş Y.

• Kocaeli University, Mathematics Department, 41380 Izmit, Turkey

Bibliografia

• [1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1972.
• [2] L. Carlitz, Weighted Stirling Numbers of the first and second kind-I, Fibonacci Quart. 18(2) (1980), 147–162.
• [3] L. Carlitz, Weighted Stirling Numbers of the first and second kind-II, Fibonacci Quart. 18(3) (1980), 242–257.
• [4] N. Gauthier, Convolving the mth powers of the consecutive integers with the general Fibonacci sequence using Carlitz’s weighted Stirling polynomials of the second kind, Fibonacci Quart. 42(4) (2004), 306–313.
• [5] E. Kılıç, H. Prodinger, Some double binomial sums related to Fibonacci, Pell and generalized order-k Fibonacci numbers, Rocky Mountain J. Math. 43(3) (2013), 975–987.
• [6] E. Kılıç, Y. Ulutaş, N. Ömür, Formulas for weighted binomial sums with the powers of terms of binary recurrences, Miskolc Mathematical Notes 13(1) (2012), 53–65.
• [7] E. Kılıç, N. Ömür, Y. Ulutaş, Binomial sums whose coefficients are products of terms of binary sequences, Utilitas Math. 84 (2011), 45–52.
• [8] R. Witula, Binomials transformation formulae of scaled Lucas numbers, Demonstratio Math. 46 (2013), 15–27.
• [9] R. Wituła, D. Słota, Central trinomial coefficients and convolution type identities, Congr. Numer. 201 (2010), 109–126.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.