[PDF] Top 20 On modified degenerate Carlitz q Bernoulli numbers and polynomials
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On modified degenerate Carlitz q Bernoulli numbers and polynomials
... weighted q-Bernoulli numbers and ...Fully degenerate poly-Bernoulli numbers and ...J-J: Degenerate q-Changhee ...DV: Degenerate q-Euler ... See full document
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Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)
... twisted q-Bernoulli polynomials under the symmetric group of degree ...the q-Bernoulli polynomials and numbers with weight α and showed some interesting ...the ... See full document
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Modified Degenerate Carlitz’s q-Bernoulli Polynomials and Numbers with Weight (α, β)
... twisted q-Bernoulli polynomials under the symmetric group of degree ...the q-Bernoulli polynomials and numbers with weight α and showed some interesting ...the ... See full document
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Some results for the q Bernoulli, q Euler numbers and polynomials
... introduced q-analogues of the Bernoulli numbers and ...on q-analogue of the Bernoulli, Euler numbers, and polynomials can be found in Choi et ... See full document
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Symmetric identities for Carlitz’s q Bernoulli numbers and polynomials
... on Carlitz q-Bernoulli numbers and ...B: q-Bernoulli numbers and q-Bernoulli polynomials ...J: q-Analogue of Riemann’s ζ function and ... See full document
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On the degenerate \((h,q)\) Changhee numbers and polynomials
... (h, q)-extension of the Bernoulli numbers and polynomials with the aid of q-Volkenborn integration, and Simsek gave the Witt-formula for (h, q)-Bernoulli numbers in ... See full document
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Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials
... the degenerate Euler ..., Carlitz [1, 2] studied the higher-order degenerate Bernoulli polynomials and the higher-order degenerate Euler polynomials which are defined by ... See full document
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The modified degenerate q Bernoulli polynomials arising from p adic invariant integral on \(\mathbb{Z} {p}\)
... modified degenerate Bernoulli polynomials, which are different from Carlitz’s degenerate Bernoulli polynomials (see Dolgy et ...modified degenerate q-Bernoulli ... See full document
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Some new identities on the twisted carlitz's q bernoulli numbers and q bernstein polynomials
... Carlitz’s q -Bernoulli numbers using p -adic q - integral on ℤ p ...Carlitz’s q -Bernoulli numbers, we investigate some properties for the twisted Carlitz’s q ... See full document
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A NOTE ON TYPE 2 DEGENERATE MULTI-POLY-BERNOULLI POLYNOMIALS AND NUMBERS
... 1956, Carlitz [1] considered a degenerate form of the well-known Staudt-Clausen theorem and then, in 1979, gave the degenerate versions of the Bernoulli, Stirling and Eulerian numbers ... See full document
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q Bernoulli numbers and q Bernoulli polynomials revisited
... Since Carlitz brought out the concept of the q-extension of Bernoulli numbers and polynomials, many mathematicians have studied q-Bernoulli numbers and ... See full document
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On q analogs of degenerate Bernoulli polynomials
... The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see Carlitz in ... See full document
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A note on Carlitz q Bernoulli numbers and polynomials
... two-variable q - L - function that is a q -analog of the two-variable L ...two-variable q-L -functions at nonpositive integers and study their properties when q tends to ... See full document
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A note on modified degenerate q Daehee polynomials and numbers
... 17. Kim, T.: On explicit formulas of p-adic q – L-functions. Kyushu J. Math. 48(1), 73–86 (1994) 18. Kim, T.: On p-adic q-Bernoulli numbers. J. Korean Math. Soc. 37(1), 21–30 (2000) 19. Kim, ... See full document
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Some identities on the twisted q Bernoulli numbers and polynomials with weight α
... By using the p-adic q-integral on Zp , we give some identities and relations on the twisted q-Bernoulli numbers and polynomials with weight α.... Jang Journal of Inequalities and Applica[r] ... See full document
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Applications of q-Umbral Calculus to Modi ed Apostol Type q-Bernoulli Polynomials
... type q-Bernoulli poly- ...type q-Bernoulli polynomials are ...aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications ... See full document
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Generalizations of Bernoulli numbers and polynomials
... of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the gen- eralized Bernoulli numbers B n (a,b) are generalized to the one B n (x;a,b,c) which is called the ... See full document
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Unified (p, q) -analog of Apostol type polynomials of order a
... (p; q)-analog of Apostol type polynomials of order ...(p; q)-Stirling numbers of the second kind of order v, a correlation between these numbers and uni…ed (p; q)-analog of ... See full document
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... of q-Hermite- Fubini numbers and polynomials by combining the q-Hermite polynomials and q- Fubini ...these numbers and polynomi- als, we derive some alternative summation ... See full document
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10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums
... (1.9) If we take a = 1, b = c = e in (1.7), (1.8) and (1.9) respectively, we have (1.4), (1.5) and (1.6). Obviously, when we set λ = 1, α = 1, a = 1, b = c = e in (1.7), (1.8) and (1.9), we have classical ... See full document
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