On Stirling numbers

• Authors: V. Barrera-Figueroa , J. López-Bonilla , R. López-Vázquez , S. Vidal-Beltrán
• Languages of publication: EN

Abstracts

EN

We exhibit an approach for the recursive formula obtained by Cereceda for the sums of powers of integers. Besides, we show that the definitions of Janjic for the Stirling numbers are consequences of the formulas of Hoppe and Quaintance-Gould.

Keywords

EN

Generalized chain rule of differentiation; Hoppe’s formula; Stirling and Bernoulli numbers; Sums of powers of integers

Discipline

• PHYSICS: PHYSICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World Scientific News
• Year: 2018
• Volume: 98
• Pages: 228-232

Contributors

author

V. Barrera-Figueroa

• SEPI-UPIITA, Instituto Politécnico Nacional, Posgrado en Tecnología Avanzada, Av. IPN 2580, Col. Barrio la Laguna 07340, CDMX, México

author

J. López-Bonilla

• ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista 07738, CDMX, México

author

R. López-Vázquez

• ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista 07738, CDMX, México

author

S. Vidal-Beltrán

• ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, Col. Lindavista 07738, CDMX, México

References

• [1] J. Quaintance, H. W. Gould, Combinatorial identities for Stirling numbers, World Scientific, Singapore (2016) Chap. 1.
• [2] V. Barrera-Figueroa, J. López-Bonilla, R. López-Vázquez, Prespacetime Journal 8(5) (2017) 572-574.
• [3] J. López-Bonilla, B. Man Tuladhar, O. Salas-Torres, Kathmandu Univ. J. of Science, Eng. & Tech. 13(1) (2017) 95-97.
• [4] J. L. Cereceda, Int. Math. Forum 9(17) (2014) 785-795.
• [5] J. López-Bonilla, R. López-Vázquez, S. Vidal-Beltrán, Prespacetime Journal 8(2) (2017) 223-225.
• [6] A. Iturri-Hinojosa, J. López-Bonilla, R. López-Vázquez, Prespacetime Journal 8(9) (2017) 1173-1175.
• [7] A. Iturri-Hinojosa, J. López-Bonilla, R. López-Vázquez, O. Salas-Torres, BAOJ Phys. 2(1) (2017) 3-5.
• [8] M. Janjic, arXiv: 0806.2366v1 [math.CO] 14 Jun 2008.
• [9] H. W. Gould, Utilitas Mathematica 61 (2002) 97-106.
• [10] W. P. Johnson, The Math. Assoc. of America 109 (2002) 217-234.
• [11] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete mathematics, Addison-Wesley, Reading, MA, USA (1994) Chap. 6.
• [12] D. Knuth, Selected papers on discrete mathematics, Center for the study of language and information, Leland Stanford Junior University (2003) Chap. 4.

• Document Type: article