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Year 2021, Volume: 8 Issue: 4, 402 - 410, 30.12.2021

Neslıhan Kılar Yılmaz Şimşek

https://doi.org/10.54287/gujsa.980263
Cited By: 1

Abstract

References

  • Belbachir, H., Rahmani, M., & Sury, B. (2011). Sums involving moments of reciprocals of binomial coefficients. Journal of Integer Sequences, 14(6), Article 11.6.6.
  • Comtet, L. (1974). Advanced Combinatorics: The Art of Finite and Infinite Expansions. Dordrecht and Boston: D. Reidel Publishing.
  • Kilar, N. (2017). Fubini Type Numbers and Their Generating Functions. MSc Thesis in Mathematics, Akdeniz University, Antalya.
  • Kilar, N. (2021). Combinatorial sums and identities associated with functional equations of generating functions for Fubini type polynomials. Preprint.
  • Kilar, N., & Simsek, Y. (2017). A new family of Fubini numbers and polynomials associated with Apostol-Bernoulli numbers and polynomials. Journal of the Korean Mathematical Society, 54(5), 1605–1621.
  • Kilar, N., & Simsek, Y. (2019a). Some relationships between Fubini type polynomials and other special numbers and polynomials. AIP Conference Proceedings, 2116(100017), 100017.1–100017.4
  • Kilar, N., & Simsek, Y. (2019b). Identities and relations for Fubini type numbers and polynomials via generating functions and p-adic integral approach. Publications de l’Institut Mathématique, 106(120), 113–123.
  • Kilar, N., & Simsek, Y. (2021). Formulas and relations of special numbers and polynomials arising from functional equations of generating functions. Montes Taurus Journal of Pure and Applied Mathematics, 3(1), 106–123.
  • Kim, T. (2002a). q-Volkenborn integration. Russian Journal of Mathematical Physics, 19, 288–299.
  • Kim, T. (2002b). An invariant p-adic integral associated with Daehee numbers. Integral Transforms and Special Functions, 13(1), 65–69.
  • Kim, T. (2005). A note on q-Volkenborn integration. Proceedings of the Jangjeon Mathematical Society, 8(1), 13–17.
  • Kim, T. (2007). On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Z_p at q = -1. Journal of Mathematical Analysis and Applications, 331(2), 779–792.
  • Kim, D. S., & Kim, T. (2013). Daehee numbers and polynomials. Applied Mathematical Sciences (Ruse), 7 (120), 5969–5976.
  • Kim, D. S., & Kim, T. (2018). Some p-adic integrals on Z_p associated with trigonometric functions. Russian Journal of Mathematical Physics, 25(3), 300–308.
  • Kim, D. S., Kim, T., & Seo, J. (2013). A note on Changhee numbers and polynomials. Advanced Studies in Theoretical Physics, 7, 993–1003.
  • Kim, T., Kim, D.S., Jang, G.-W., & Kwon, J. (2018). Symmetric identities for Fubini polynomials. Symmetry, 10, 219.
  • OEIS, The On-Line Encyclopedia of Integer Sequences (2021). (Accessed: 14/10/2021) oeis.org/A000670.
  • Rainville, E. D. (1960). Special Functions. New York: The Macmillan Company.
  • Riordan, J. (1958). An Introduction to Combinatorial Analysis. New York: John Wiley Sons Inc.
  • Schikhof, W. H. (1984). Ultrametric Calculus: An Introduction to p-adic Analysis. Cambridge Studies in Advanced Mathematics 4, Cambridge: Cambridge University Press.
  • Simsek, Y. (2013). Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications. Fixed Point Theory and Applications, 87(2013), 1–28.
  • Simsek, Y. (2016). Apostol type Daehee numbers and polynomials. Advanced Studies in Contemporary Mathematics, 26, 555–566.
  • Simsek, Y. (2019). Explicit formulas for p-adic integrals: Approach to p-adic distributions and some families of special numbers and polynomials. Montes Taurus Journal of Pure and Applied Mathematics, 1(1), 1–76.
  • Simsek, Y. (2021). Interpolation functions for new classes special numbers and polynomials via applications of p-adic integrals and derivative operator. Montes Taurus Journal of Pure and Applied Mathematics, 3(1), 38–61.
  • Srivastava, H. M., & Choi, J. (2012). Zeta and q-Zeta Functions and Associated Series and Integrals. Amsterdam: Elsevier.
  • Srivastava, H. M., & Kızılateş, C. (2019). A parametric kind of the Fubini-type polynomials. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RACSAM) 113, 3253–3267.

Formulae to Fubini Type Numbers emerge from Application of p-adic Integrals

Year 2021, Volume: 8 Issue: 4, 402 - 410, 30.12.2021

Neslıhan Kılar Yılmaz Şimşek

https://doi.org/10.54287/gujsa.980263
Cited By: 1

Abstract

The aim of this manuscript is to examine and survey various formulae for Fubini type numbers and polynomials with application of the p-adic integrals to some special polynomials. Relations and formulae related to the Fubini type numbers and polynomials, the Bernoulli numbers, the Euler numbers, Stirling type numbers, and combinatorial numbers are given. Moreover, by using generating functions with their functional equations, some new formulae including the Hermite polynomials, the Fubini type polynomials, and the Lah numbers are given. Finally, remarks on the results of this manuscript are presented.

Keywords

Bernoulli Polynomials and Numbers Fubini Type Polynomials and Numbers Special Polynomials and Numbers Generating Function p-adic Integral

References

  • Belbachir, H., Rahmani, M., & Sury, B. (2011). Sums involving moments of reciprocals of binomial coefficients. Journal of Integer Sequences, 14(6), Article 11.6.6.
  • Comtet, L. (1974). Advanced Combinatorics: The Art of Finite and Infinite Expansions. Dordrecht and Boston: D. Reidel Publishing.
  • Kilar, N. (2017). Fubini Type Numbers and Their Generating Functions. MSc Thesis in Mathematics, Akdeniz University, Antalya.
  • Kilar, N. (2021). Combinatorial sums and identities associated with functional equations of generating functions for Fubini type polynomials. Preprint.
  • Kilar, N., & Simsek, Y. (2017). A new family of Fubini numbers and polynomials associated with Apostol-Bernoulli numbers and polynomials. Journal of the Korean Mathematical Society, 54(5), 1605–1621.
  • Kilar, N., & Simsek, Y. (2019a). Some relationships between Fubini type polynomials and other special numbers and polynomials. AIP Conference Proceedings, 2116(100017), 100017.1–100017.4
  • Kilar, N., & Simsek, Y. (2019b). Identities and relations for Fubini type numbers and polynomials via generating functions and p-adic integral approach. Publications de l’Institut Mathématique, 106(120), 113–123.
  • Kilar, N., & Simsek, Y. (2021). Formulas and relations of special numbers and polynomials arising from functional equations of generating functions. Montes Taurus Journal of Pure and Applied Mathematics, 3(1), 106–123.
  • Kim, T. (2002a). q-Volkenborn integration. Russian Journal of Mathematical Physics, 19, 288–299.
  • Kim, T. (2002b). An invariant p-adic integral associated with Daehee numbers. Integral Transforms and Special Functions, 13(1), 65–69.
  • Kim, T. (2005). A note on q-Volkenborn integration. Proceedings of the Jangjeon Mathematical Society, 8(1), 13–17.
  • Kim, T. (2007). On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Z_p at q = -1. Journal of Mathematical Analysis and Applications, 331(2), 779–792.
  • Kim, D. S., & Kim, T. (2013). Daehee numbers and polynomials. Applied Mathematical Sciences (Ruse), 7 (120), 5969–5976.
  • Kim, D. S., & Kim, T. (2018). Some p-adic integrals on Z_p associated with trigonometric functions. Russian Journal of Mathematical Physics, 25(3), 300–308.
  • Kim, D. S., Kim, T., & Seo, J. (2013). A note on Changhee numbers and polynomials. Advanced Studies in Theoretical Physics, 7, 993–1003.
  • Kim, T., Kim, D.S., Jang, G.-W., & Kwon, J. (2018). Symmetric identities for Fubini polynomials. Symmetry, 10, 219.
  • OEIS, The On-Line Encyclopedia of Integer Sequences (2021). (Accessed: 14/10/2021) oeis.org/A000670.
  • Rainville, E. D. (1960). Special Functions. New York: The Macmillan Company.
  • Riordan, J. (1958). An Introduction to Combinatorial Analysis. New York: John Wiley Sons Inc.
  • Schikhof, W. H. (1984). Ultrametric Calculus: An Introduction to p-adic Analysis. Cambridge Studies in Advanced Mathematics 4, Cambridge: Cambridge University Press.
  • Simsek, Y. (2013). Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications. Fixed Point Theory and Applications, 87(2013), 1–28.
  • Simsek, Y. (2016). Apostol type Daehee numbers and polynomials. Advanced Studies in Contemporary Mathematics, 26, 555–566.
  • Simsek, Y. (2019). Explicit formulas for p-adic integrals: Approach to p-adic distributions and some families of special numbers and polynomials. Montes Taurus Journal of Pure and Applied Mathematics, 1(1), 1–76.
  • Simsek, Y. (2021). Interpolation functions for new classes special numbers and polynomials via applications of p-adic integrals and derivative operator. Montes Taurus Journal of Pure and Applied Mathematics, 3(1), 38–61.
  • Srivastava, H. M., & Choi, J. (2012). Zeta and q-Zeta Functions and Associated Series and Integrals. Amsterdam: Elsevier.
  • Srivastava, H. M., & Kızılateş, C. (2019). A parametric kind of the Fubini-type polynomials. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RACSAM) 113, 3253–3267.
There are 26 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Neslıhan Kılar 0000-0001-5797-6301

Yılmaz Şimşek 0000-0002-0611-7141

Publication Date December 30, 2021
Submission Date August 8, 2021
Published in Issue Year 2021 Volume: 8 Issue: 4

Cite

APA Kılar, N., & Şimşek, Y. (2021). Formulae to Fubini Type Numbers emerge from Application of p-adic Integrals. Gazi University Journal of Science Part A: Engineering and Innovation, 8(4), 402-410. https://doi.org/10.54287/gujsa.980263

Cited By

Certain Finite Sums Pertaining to Leibnitz, Harmonic and Other Special Numbers
Gazi University Journal of Science Part A: Engineering and Innovation
https://doi.org/10.54287/gujsa.1134534
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