On some summation formulas

• Autorzy: Kim Taekyun , Kim Dae San , Lee Hyunseok , Kwon Jongkyum

Identyfikatory

DOI

10.1515/dema-2022-0003

• Języki publikacji: EN

Abstrakty

EN

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals.

Słowa kluczowe

EN

summation formulae; harmonic numbers of order r

PL

formuła sumacyjna; liczba harmoniczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 1--7
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Kim Taekyun

• Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

autor

Kim Dae San

• Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

autor

Lee Hyunseok

• Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

autor

Kwon Jongkyum

• Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea

Bibliografia

• [1] E. T. Whittaker and G. N. Watson, A course of modern analysis, an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Reprint of the fourth (1927) edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996.
• [2] G. E. Andrews, R. Askey, and R. Roy, Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999.
• [3] S. Araci, M. Acikgoz, C. Özel, H. M. Srivastava, and T. Diagana, Recent trends in special numbers and special functions and polynomials, Int. J. Math. Math. Sci. 2015 (2015), 573893.
• [4] T. Kim and D. S. Kim, Some identities on truncated polynomials associated with degenerate Bell polynomials, Russ. J. Math. Phys. 28 (2021), no. 3, 342–355.
• [5] W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, Translated by John Wermer, Chelsea Publishing Company, New York, N.Y., 1949.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).