Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 15 Sayı: 1, 203 - 211, 30.06.2023
https://doi.org/10.47000/tjmcs.1242781

Öz

Kaynakça

  • Abramowitz, M., Stegun, I.A., Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Courier Corporation, USA, 1972.
  • Apostol, T.M., On the Lerch zeta function, Pacic J. Math., 1(1951), 161–167.
  • Apostol, T.M., Modular Functions and Dirichlet Series in Number Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1976.
  • Dattoli, G., Germano, B., Licciardi, S., Martinelli, M. R., Umbral methods and harmonic numbers, Axioms, 7(2018), 1–9.
  • Kuş, S., Tuglu, N., Kızılates¸, C., A study of harmonic Fibonacci polynomials associated with Bernoulli-F and Euler–Fibonacci polynomials, Indian J. Pure Appl. Math., to appear.
  • Luo, Q.M., Some recursion formulae and relations for Bernoulli numbers and Euler numbers of higher order, Adv. Stud. Contemp. Math. (Kyungshang), 10(2005), 63–70.
  • Luo, Q.M., Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. Math. 10(2006), 917–925.
  • Luo, Q.M., The multplication formulas for the Apostol-Bernoulli and Apostol Euler polynomials of higher order, Integ. Trans. and Special Func., 20(2009), 377–391.
  • Luo, Q.M., Srivastava, H.M., Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308(2005), 290-302.
  • Luo, Q.M., Srivastava, H.M., Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl., 51(2006), 631-642.
  • Özvatan, M., Generalized Golden-Fibonacci Calculus and Applications, Master Thesis, The Graduate School of Engineering and Sciences of Izmir Institute of Technology, ˙Izmir, 2018.
  • Pashaev, O.K., Nalci, S., Golden quantum oscillator and Binet Fibonacci calculus, J Phys A: Math Theor., 45(2012), 015303.
  • Srivastava, H.M., Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc., 129(2000), 77-84.
  • Srivastava, H.M., Pinter, A., Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17(2004), 375-380.
  • Srivastava, H.M., Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001.
  • Tuglu N., Kızılates¸ C., Kesim, S., On the harmonic and hyperharmonic Fibonacci numbers, Advances in Difference Equations, 2015(2015), 297.

Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions

Yıl 2023, Cilt: 15 Sayı: 1, 203 - 211, 30.06.2023
https://doi.org/10.47000/tjmcs.1242781

Öz

In this article, the Apostol Bernoulli-Fibonacci polynomials are defined and various properties of Apostol Bernoulli-Fibonacci polynomials are obtained. Furthermore, Apostol Euler-Fibonacci numbers and polynomials are found. In addition, harmonic-based F exponential generating functions are defined for Apostol Bernoulli-Fibonacci numbers and Apostol Euler-Fibonacci numbers.

Kaynakça

  • Abramowitz, M., Stegun, I.A., Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Courier Corporation, USA, 1972.
  • Apostol, T.M., On the Lerch zeta function, Pacic J. Math., 1(1951), 161–167.
  • Apostol, T.M., Modular Functions and Dirichlet Series in Number Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1976.
  • Dattoli, G., Germano, B., Licciardi, S., Martinelli, M. R., Umbral methods and harmonic numbers, Axioms, 7(2018), 1–9.
  • Kuş, S., Tuglu, N., Kızılates¸, C., A study of harmonic Fibonacci polynomials associated with Bernoulli-F and Euler–Fibonacci polynomials, Indian J. Pure Appl. Math., to appear.
  • Luo, Q.M., Some recursion formulae and relations for Bernoulli numbers and Euler numbers of higher order, Adv. Stud. Contemp. Math. (Kyungshang), 10(2005), 63–70.
  • Luo, Q.M., Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. Math. 10(2006), 917–925.
  • Luo, Q.M., The multplication formulas for the Apostol-Bernoulli and Apostol Euler polynomials of higher order, Integ. Trans. and Special Func., 20(2009), 377–391.
  • Luo, Q.M., Srivastava, H.M., Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308(2005), 290-302.
  • Luo, Q.M., Srivastava, H.M., Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl., 51(2006), 631-642.
  • Özvatan, M., Generalized Golden-Fibonacci Calculus and Applications, Master Thesis, The Graduate School of Engineering and Sciences of Izmir Institute of Technology, ˙Izmir, 2018.
  • Pashaev, O.K., Nalci, S., Golden quantum oscillator and Binet Fibonacci calculus, J Phys A: Math Theor., 45(2012), 015303.
  • Srivastava, H.M., Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc., 129(2000), 77-84.
  • Srivastava, H.M., Pinter, A., Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17(2004), 375-380.
  • Srivastava, H.M., Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001.
  • Tuglu N., Kızılates¸ C., Kesim, S., On the harmonic and hyperharmonic Fibonacci numbers, Advances in Difference Equations, 2015(2015), 297.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Elif Gülal Bu kişi benim 0000-0003-1145-246X

Naim Tuglu 0000-0002-7277-0034

Yayımlanma Tarihi 30 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 15 Sayı: 1

Kaynak Göster

APA Gülal, E., & Tuglu, N. (2023). Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. Turkish Journal of Mathematics and Computer Science, 15(1), 203-211. https://doi.org/10.47000/tjmcs.1242781
AMA Gülal E, Tuglu N. Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. TJMCS. Haziran 2023;15(1):203-211. doi:10.47000/tjmcs.1242781
Chicago Gülal, Elif, ve Naim Tuglu. “Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions”. Turkish Journal of Mathematics and Computer Science 15, sy. 1 (Haziran 2023): 203-11. https://doi.org/10.47000/tjmcs.1242781.
EndNote Gülal E, Tuglu N (01 Haziran 2023) Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. Turkish Journal of Mathematics and Computer Science 15 1 203–211.
IEEE E. Gülal ve N. Tuglu, “Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions”, TJMCS, c. 15, sy. 1, ss. 203–211, 2023, doi: 10.47000/tjmcs.1242781.
ISNAD Gülal, Elif - Tuglu, Naim. “Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions”. Turkish Journal of Mathematics and Computer Science 15/1 (Haziran 2023), 203-211. https://doi.org/10.47000/tjmcs.1242781.
JAMA Gülal E, Tuglu N. Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. TJMCS. 2023;15:203–211.
MLA Gülal, Elif ve Naim Tuglu. “Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions”. Turkish Journal of Mathematics and Computer Science, c. 15, sy. 1, 2023, ss. 203-11, doi:10.47000/tjmcs.1242781.
Vancouver Gülal E, Tuglu N. Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. TJMCS. 2023;15(1):203-11.