Keywords: Trigonometric sums; Computational formula; Identity; Dirichlet L-functions; Bernoulli numbers; 11B68; 11M06;
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Keywords: Bernoulli numbers of the second kind; Bernoulli polynomials of the second kind; Cauchy numbers; Cauchy polynomials; Convolution identity; 11B83; 11B68; 05A15;
Keywords: 11B68; 78A70; 26A33; Euler's numbers; Biological application; Fractional logistic equation;
Keywords: 11B68; 11C20; 11M06; Bernoulli number; Bernoulli polynomial; Riemann zeta function; Euler number; Euler polynomial; Alternating zeta function; Double zeta values; Hurwitz zeta function; Lerch zeta function; Polygamma function; Ramanujan polynomial; Bernou
Keywords: primary; 11B83; secondary; 11B68; Product of primes; Bernoulli polynomials; Denominator; Sum of base-p digits; p-Adic valuation of polynomials;
Keywords: 11B75; 11B73; 11B68; Generalized harmonic numbers; Quantum distribution moments; Stirling numbers; Generating relations; Sum rules; Pochhammer symbol;
Keywords: 11B37; 11B68; 11M06; 11M35; Bernoulli numbers and polynomials; Recurrence relations; Saalschütz-Gelfand's formula; Von Ettingshausen-Stern's formula; Riemann zeta-function; Dirichlet L-series;
Keywords: Euler polynomials and numbers; Changhee polynomials and numbers; twisted Euler polynomials; twisted Changhee polynomials; 11B68; 11S40;
Keywords: 11B25; 11B68; 11B73; Arithmetic progressions; Power sums; Stirling numbers; r-Whitney numbers; Bernoulli polynomials;
Keywords: 05E05; 11B68; 11B75Bernoulli polynomials; Jacobi–Stirling numbers; Legendre–Stirling numbers; Chebyshev–Stirling numbers
Keywords: 05A19; 11B68; 11B73; 15A09; 26A24; 33B10Explicit expression; Faà di Bruno’s formula; Stirling number; Exponential function; Apostol–Bernoulli number; Fubini number
Keywords: 11B68; 11B73; 33B10Explicit formula; Euler polynomial; Two-parameter Euler polynomial; Stirling number of the second kind; Identity; Exponential function
Keywords: 11B68; 11B73; 26A24; 33B10; 34A30; 39B22; Explicit formula; Bernoulli number; Identity; Stirling number of the second kind; Exponential function; Combinatorial number;
Keywords: primary; 11B68; Hypergeometric Bernoulli polynomial; Appell sequence; Convolution; Sums of products;
Keywords: 11B68; 11S40Bernoulli numbers; Bernoulli polynomials; Riemann zeta function; Recurrences
Keywords: 05A15; 05A30; 11B68; 33B10Entringer numbers; Poupard numbers; Tangent numbers; Secant numbers; Linear refinement; Entringer–Poupard matrix sequence; Matrix refinement; Alternating permutations; Three-variate generating function calculus; Seidel and skew S
A new condition equivalent to the Ankeny-Artin-Chowla conjecture
Keywords: primary; 11B39; secondary; 11R27; 11R11; 11B37; 11B68; Ankeny-Artin-Chowla conjecture; Fundamental unit; Lucas polynomial;
On several q-special matrices, including the q-Bernoulli and q-Euler matrices
Keywords: primary; 11B68; 11B73; secondary; 33D99; 05A40; Keywords q-Bernoulli matrix; q-Cauchy matrix; Bernoulli complementary argument theorem; q-Appell polynomial; Arponen polynomial matrix approach; q-Stirling number;
Finite difference of the overpartition function
Keywords: 05A20; 11B68; Integer partition; Overpartition; Log-concave; Finite difference;
Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
Keywords: primary; 11B68; secondary; 42C10; 33C10; 11M41; Appell-Dunkl sequences; Bernoulli-Dunkl polynomials; Apostol-Euler-Dunkl polynomials; Dunkl kernel; Fourier-Dunkl series; Zeros of Bessel functions; Rayleigh functions;
Proof of two conjectural supercongruences involving Catalan-Larcombe-French numbers
Keywords: primary; 11B65; 11B68; secondary; 05A10; 11A07; Central binomial coefficients; Supercongruence; Harmonic numbers;
Some identities for multiple Hurwitz zeta values
Keywords: primary; 11M32; 11M35; secondary; 11B68; Multiple Hurwitz zeta values; Multiple Hurwitz zeta-star values; Generating function;
(Ï,q)-Volkenborn integration
Keywords: 05A30; 11B65; 11B68; 11S23; q-Volkenborn integral; Carlitz's q-Bernoulli polynomials; (Ï,q)-calculus; p-adic number;
The p-adic analytic Dedekind sums
Keywords: 11F20; 11B68; 11S80; 11M35; p-adic integral; p-adic Hurwitz zeta function; Dedekind sum; Bernoulli polynomial; Euler polynomial;
The p-adic Arakawa-Kaneko-Hamahata zeta functions and poly-Euler polynomials
Keywords: 11M41; 11M35; 11S80; 11B68; p-Adic analysis; p-Adic Arakawa-Kaneko-Hamahata zeta functions; Poly-Euler polynomials; Sums of products identity;
Sum formulas of multiple zeta values with arguments multiples of a common positive integer
Keywords: primary; 11M32; 11M35; secondary; 11B68; Multiple zeta values; Multiple zeta-star values;
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
Keywords: primary; 05A10; 05A15; 11B37; 11B39; 11B68; 11B83; 11M35; 26C05; 26C10; secondary; 33C05; 34A99; 35A99; Generating functions; Functional equations; Partial differential equations; Hypergeometric functions; Hurwitz-Lerch zeta functions; Apostol-Bernoul
Supercongruences involving dual sequences
Keywords: primary; 11A07; 11B65; secondary; 05A10; 05A19; 11B68; 11B75; p-adic congruences; Binomial coefficients; Combinatorial identities; Dual sequences;
Degenerate Mittag-Leffler polynomials
Keywords: Degenerate Mittag-Leffler polynomials; Falling factorial polynomials; Bernoulli polynomials; Frobenius-Euler polynomials; Umbral calculus; 05A19; 05A40; 11B68; 11B83; 65D20; 65Q30;
On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions
Keywords: 11F20; 11B68; 65B15; Dedekind sum; Boole summation formula; Euler polynomial; Quasi-periodic Euler functions;
Inverse of some matrix related to double zeta values of odd weight
Keywords: 11B65; 11B68; 11M32Double zeta value of odd weight; Bernoulli number identity
Lower triangular Toeplitz–Ramanujan systems whose solution yields the Bernoulli numbers
Keywords: 11B68; 11Y55; 15A06; 15A09; 15A24; 15B05; 15B99; 65F05Bernoulli numbers; Triangular Toeplitz matrices
Integration of a Dirac comb and the Bernoulli polynomials
Keywords: 34A36; 37B55; 11B68; 70G60Dirac comb; Piecewise-smooth; Differential equations; Bernoulli polynomials
On the families of q-Euler polynomials and their applications
Keywords: 05A10; 11B65; 11B68; 11B73Euler numbers and polynomials; q-Euler numbers and polynomials; Weighted q-Euler numbers and polynomials; Weighted q-Euler-Zeta function; p-adic q -integral on ZpZp
A note on the pseudo Stolarsky type inequality for the g¯-integral
Keywords: Ï-â-decomposable measure; Pseudo-integral; Interval-representable pseudo-operations; Stolarsky type inequality; 28E10; 28E20; 03E72; 26E50; 11B68;
On the mean values of Dirichlet L-functions
Keywords: 11M06; 11F20; 11B68; L-function; Character sum; Gauss sum; Bernoulli polynomial;
Supercongruences motivated by e
Keywords: primary; 11B65; secondary; 05A10; 11A07; 11B68; Supercongruences; Binomial coefficients; Bernoulli numbers;
Poly-Bernoulli numbers and polynomials with a q parameter
Keywords: 11B68; 11B73; 11B75Poly-Bernoulli and poly-Cauchy numbers and polynomials; Weighted Stirling numbers; λ-Stirling numbers; Congruences
On p-Bernoulli numbers and polynomials
Keywords: 11B68; 65D20; 33C05Bernoulli numbers and polynomials; Euler–Zagier's multiple zeta function; Gaussian hypergeometric function; Three-term recurrence relation
On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials
Keywords: 11F20; 11B68; 65B15; 44A10Dedekind sums; Bernoulli polynomials; Bernoulli numbers; Euler–MacLaurin formula; Laplace transform
Extended Bernoulli and Stirling matrices and related combinatorial identities
Keywords: 05A10; 05A19; 11B68; 11B73Bernoulli polynomials; Stirling numbers; Hyperharmonic numbers; Pascal matrix; Bernoulli matrix; Stirling matrix
Congruences arising from Apéry-type series for zeta values
Keywords: 11B65; 05A10; 11B68; 11A07; 33F10; 11B39; 11M06; Congruence; Creative telescoping; WZ pair; Finite central binomial sum; Multiple harmonic sum; Bernoulli number; Apéry-like series; Zeta value;
On p-adic Hurwitz-type Euler zeta functions
Keywords: 11E95; 11B68; 11S80; 11M35; Euler number and polynomial; p-adic integral; p-adic Hurwitz-type Euler zeta function;
Padé approximation and Apostol–Bernoulli and Apostol–Euler polynomials
Keywords: 11B68; 41A21Apostol–Bernoulli polynomials; Apostol–Euler polynomials; Bernoulli numbers; Euler numbers; Padé approximants
q-Hardy-Berndt type sums associated with q-Genocchi type zeta and q-l-functions
Keywords: primary; 11F20; 11S80; secondary; 30B40; 11B68; 11S40; 30B50; 44A05; q-Bernoulli numbers and polynomials; q-Genocchi zeta; q-l series; p-adic interpolation function; q-Dedekind type sums; q-Hardy-Berndt type sums;
A numerical computation of the structure of the roots of q-Bernoulli polynomials
Keywords: 11B68; 11S40; Bernoulli polynomials; Bernoulli numbers; q-Bernoulli polynomials; q-Bernoulli numbers; Generating functions of q-Bernoulli numbers; Roots of the q-Bernoulli polynomials; Reflection symmetries of the q-Bernoulli polynomials;
Notes on degenerate numbers
Keywords: 11B68; 11B73; 11B37Potential and Bell polynomials; Bernoulli and Stirling numbers
Explicit evaluations of extended Euler sums
Keywords: primary 11M35; 11B68; secondary 11M06; 40B05Zeta function; Bernoulli polynomial; Euler sum
On explicit formulae for Bernoulli numbers and their counterparts in positive characteristic
Keywords: 11B68; 11R58; Bernoulli numbers; Bernoulli-Carlitz numbers; Hasse-Teichmüller derivatives; Carlitz exponential;
On the properties of Newton-Euler pairs
Keywords: 11B83; 15A15; 11B68; 05A17; 11A25; 11B73; 11B65; 11B39; Newton-Euler pair; Newton-Euler sequence; The sum of divisors; The number of partitions; Bernoulli numbers;