Generalizations of poly-Bernoulli and poly-Cauchy numbers

Arakawa, T., Ibukiyama, T., Kaneko, M.: Bernoulli Numbers and Zeta Functions. Springer Monographs in Mathematics. Springer, Tokyo (2014)

Arakawa, T., Kaneko, M.: On poly-Bernoulli numbers. Comment. Math. Univ. St. Paul 48(2), 159–167 (1999)

Arakawa, T., Kaneko, M.: Multiple zeta values, poly-Bernoulli numbers, and related zeta functions. Nagoya Math. J. 153, 189–209 (1999)

Bayad, A., Hamahata, Y.: Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65(1), 15–24 (2011)

Brewbaker, C.: A combinatorial interpretation of the poly-Bernoulli numbres and two Fermat analogues. Integers 8(1), # A2 (2008)

Carlitz, L.: A note on Bernoulli and Euler polynomials of the second kind. Scripta Math. 25, 323–330 (1961)

Carlitz, L.: Degenerate Stirling. Bernoulli and Eulerian numbers. Util. Math. 15, 51–88 (1979)

Carlitz, L.: Weighted Stirling numbers of the first and second kind—I. Fibonacci Quart. 18(2), 147–162 (1980)

Cenkci, M., Komatsu, T.: Poly-Bernoulli numbers and polynomials with a $$q$$ q parameter. J. Number Theory 152, 38–54 (2015)

Coppo, M.-A., Candelpergher, B.: The Arakawa–Kaneko zeta functions. Ramanujan J. 22(2), 153–162 (2010)

Coppo, M.-A., Candelpergher, B.: Inverse binomial series and values of Arakawa–Kaneko zeta functions. J. Number Theory 150, 98–119 (2015)

El-Desouky, B.S., Gomaa, R.S.: Multiparameter poly-Cauchy and poly-Bernoulli numbers and polynomials (2014). arXiv:1410.5300

Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics, 2nd edn. Addison-Wesley, Reading (1994)

Howard, F.T.: Degenerate weighted Stirling numbers. Discrete Math. 57(1–2), 45–58 (1985)

Hsu, L.C., Shiue, P.J.-S.: A unified approach to generalized Stirling numbers. Adv. Appl. Math. 20(3), 366–384 (1998)

Jolany, H., Corcino, R.B.: Explicit formula for generalization of poly-Bernoulli numbers and polynomials with $$a,b,c$$ a , b , c parameters (2011). arXiv:1109.1387

Jordan, C.: Calculus of Finite Differences, 2nd edn. Chelsea, New York (1950)

Kamano, K., Komatsu, T.: Poly-Cauchy polynomials. Mosc. J. Comb. Number Theory 3(2), 61–87 (2013)

Kaneko, M.: Poly-Bernoulli numbers. J. Théor. Nombres Bordeaux 9(1), 221–228 (1997)

Knuth, D.E.: Two notes on notation. Amer. Math. Monthly 99(5), 403–422 (1992)

Komatsu, T.: Poly-Cauchy numbers with a $$q$$ q parameter. Ramanujan J. 31(3), 353–371 (2013)

Komatsu, T.: Poly-Cauchy numbers. Kyushu J. Math. 67(1), 143–153 (2013)

Komatsu, T., Laohakosol, V., Liptai, K.: A generalization of poly-Cauchy numbers and their properties. Abstr. Appl. Anal. # 179841 (2013)

Komatsu, T., Luca, F.: Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Ann. Math. Inform. 41, 99–105 (2013)

Komatsu, T., Szalay, L.: Shifted poly-Cauchy numbers. Lithuanian Math. J. 54(2), 166–181 (2014)

Launois, S.: Combinatorics of $$\fancyscript {H}$$ H -primes in quantum matrices. J. Algebra 309(1), 139–167 (2007)

Merlini, D., Sprugnoli, R., Verri, M.C.: The Cauchy numbers. Discrete Math. 306(16), 1906–1920 (2006)

Nörlund, N.E.: Vorlesungen über Differenzenrechnung. Chelsea, New York (1954)

Sánchez-Peregrino, R.: Closed formula for poly-Bernoulli numbers. Fibonacci Quart. 40(4), 362–364 (2002)

Srivastava, H.M., Choi, J.: Series Associated with the Zeta and Related Functions. Kluwer, Dordrecht (2001)

Young, P.T.: Congruences for degenerate number sequences. Discrete Math. 270(1–3), 279–289 (2003)

Young, P.T.: Symmetries of Bernoulli polynomial series and Arakawa–Kaneko zeta functions. J. Number Theory 143, 142–161 (2014)

Young, P.T.: The $$p$$ p -adic Arakawa–Kaneko zeta functions and $$p$$ p -adic Lerch transcendent. J. Number Theory 155, 13–35 (2015)