Keywords: اعداد برنولی; Trigonometric sums; Computational formula; Identity; Dirichlet L-functions; Bernoulli numbers; 11B68; 11M06;
مقالات ISI اعداد برنولی (ترجمه نشده)
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Keywords: اعداد برنولی; primary; 11B65; secondary; 05A10; Binomial coefficients; p-adic valuation; Lucas' theorem; Euler's totient theorem; Bernoulli numbers;
Keywords: اعداد برنولی; primary; 30C15; 11B83; 41A60; secondary; 11M36; 34K06; Deformed exponential function; Asymptotic expansion; Eisenstein series; Bernoulli numbers;
Keywords: اعداد برنولی; primary; 11M06; secondary; 33E99; 33B15; Riemann zeta function; Odd integer; Raabe's integral; Abel's criteria; Bernoulli numbers;
Keywords: اعداد برنولی; Harmonic sums; Polylogarithms; Bernoulli polynomials; Multi-Eulerian polynomials; Bernoulli numbers; Eulerian numbers;
Keywords: اعداد برنولی; Bernoulli polynomials; Euler polynomials; Bernoulli numbers; Euler numbers; Convolution identities
Keywords: اعداد برنولی; 11A07; 11A41Congruences; Bernoulli numbers; Harmonic sums
Keywords: اعداد برنولی; Ordinary differential equation; Bernoulli polynomials; Bernoulli numbers;
Keywords: اعداد برنولی; 11A07; 11A41Congruences; Bernoulli numbers; Modulo prime powers
Keywords: اعداد برنولی; Bernoulli polynomials; Euler polynomials; Bernoulli numbers; Euler numbers; Genocchi numbers; Convolution identities;
Keywords: اعداد برنولی; Integral transform; Trigonometric functions; Hyperbolic functions; Central binomial coefficient; Catalanʼs constant; Geometric rate of convergence; L-functions; Riemann zeta function; Hurwitz zeta function; Bernoulli polynomials; Bernoulli numbers;
Keywords: اعداد برنولی; Bernoulli numbers; Bernoulli polynomials; Euler numbers; Euler polynomials; Genocchi numbers; Genocchi polynomials; Generating functions; Maple;
More asymptotic expansions for the Barnes G-function
Keywords: اعداد برنولی; 33B15; 41A60; Asymptotic expansions; Barnes G-function; Bell polynomials; Bernoulli numbers;
Asymptotic expansions related to hyperfactorial function and Glaisher-Kinkelin constant
Keywords: اعداد برنولی; Asymptotic expansions; Hyperfactorial function; Glaisher-Kinkelin constant; Bell polynomials; Bernoulli numbers; 41A60; 11Y60;
A supercongruence involving Delannoy numbers and Schröder numbers
Keywords: اعداد برنولی; 11A07; 11B65; 11B83; 05A10Supercongruence; Delannoy numbers; Schröder numbers; Bernoulli numbers
Inequalities and asymptotic expansions for the gamma function related to Mortici's formula
Keywords: اعداد برنولی; primary; 33B15; secondary; 41A60; Gamma function; Asymptotic formula; Bernoulli numbers; Fundamental theorem of algebra; Newton's formulas;
qq-poly-Bernoulli numbers and qq-poly-Cauchy numbers with a parameter by Jackson’s integrals
Keywords: اعداد برنولی; qq-poly-Bernoulli polynomials; qq-poly-Cauchy polynomials; Jackson’s integrals; Bernoulli numbers; Cauchy numbers; Weighted Stirling numbers
Expansions of generalized Euler's constants into the series of polynomials in π−2π−2 and into the formal enveloping series with rational coefficients only
Keywords: اعداد برنولی; Generalized Euler's constants; Stieltjes constants; Stirling numbers; Factorial coefficients; Series expansion; Divergent series; Semi-convergent series; Formal series; Enveloping series; Asymptotic expansions; Approximations; Bernoulli numbers; Harmonic
On the Ramanujan-Lodge harmonic number expansion
Keywords: اعداد برنولی; Harmonic numbers; Bernoulli numbers; Asymptotic expansion; Rate of convergence; Approximations; Inequalities;
Supercongruences motivated by e
Keywords: اعداد برنولی; primary; 11B65; secondary; 05A10; 11A07; 11B68; Supercongruences; Binomial coefficients; Bernoulli numbers;
On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials
Keywords: اعداد برنولی; 11F20; 11B68; 65B15; 44A10Dedekind sums; Bernoulli polynomials; Bernoulli numbers; Euler–MacLaurin formula; Laplace transform
Asymptotic expansions of the Glaisher–Kinkelin and Choi–Srivastava constants
Keywords: اعداد برنولی; 41A60Glaisher–Kinkelin constant; Choi–Srivastava constants; Asymptotic expansion; Bernoulli numbers
Asymptotic expansions for Barnes G-function
Keywords: اعداد برنولی; primary; 33B15; secondary; 41A60; Gamma function; Barnes G-function; Bernoulli numbers; Asymptotic expansion;
Secant zeta functions
Keywords: اعداد برنولی; Secant zeta function; Bernoulli numbers; Clausen functions; Riemann zeta function
p-adic congruences motivated by series
Keywords: اعداد برنولی; primary, 11B65; secondary, 05A10, 05A19, 11A07, 11B68, 11S99p-adic congruences; Central binomial coefficients; Bernoulli numbers
Sums of reciprocals modulo composite integers
Keywords: اعداد برنولی; Lehmerʼs congruences; Fermat quotients; Euler quotients; Bernoulli numbers; Bernoulli polynomials;
A solution to an open problem on the Euler–Mascheroni constant
Keywords: اعداد برنولی; Euler–Mascheroni constant; Bernoulli numbers; Le Verrier method; Harmonic number
Asymptotic expansions related to Glaisher–Kinkelin constant based on the Bell polynomials
Keywords: اعداد برنولی; 11Y60; 40A05Asymptotic formula; Glaisher–Kinkelin constant; Bernoulli numbers; Bell polynomials; Partition function
Symmetric recurrence relations and binomial transforms
Keywords: اعداد برنولی; 05A19; 05A10; 11B68Recurrence relation; Binomial transform; Bernoulli numbers
Congruences for central binomial sums and finite polylogarithms
Keywords: اعداد برنولی; Congruences; Bernoulli numbers; Binomial coefficients; Polylogarithm; Finite sums
Remarks on asymptotic expansions for the gamma function
Keywords: اعداد برنولی; Gamma function; Bernoulli numbers; Asymptotic expansion
On the largest prime factor of numerators of Bernoulli numbers
Keywords: اعداد برنولی; Bernoulli numbers; Primes; Applications of linear forms in logarithms
Some identities for multiple zeta values
Keywords: اعداد برنولی; Multiple zeta values; Harmonic shuffle relation; Bernoulli numbers
On sums of Apéry polynomials and related congruences
Keywords: اعداد برنولی; primary, 11A07, 11B65; secondary, 05A10, 11B68, 11E25Apéry numbers and Apéry polynomials; Bernoulli numbers; Binomial coefficients; Congruences
The action of Hecke operators to families of Weierstrass-type functions and Weber-type functions and their applications
Keywords: اعداد برنولی; Generalized Dedekind eta functions; Eisenstein series; Theta functions; Hecke operators; Weierstrass type functions; Weber functions; Bernoulli numbers; Riemann zeta function
A note on sums of products of Bernoulli numbers
Keywords: اعداد برنولی; Bernoulli numbers; Hurwitz zeta functions; Multiple Hurwitz zeta functions; Sums of products; Multinomial coefficients
Asymptotic formulas for the triple Gamma function Î3 by means of its integral representation
Keywords: اعداد برنولی; Gamma, double, triple and multiple Gamma functions; Riemann Zeta function; Hurwitz (or generalized) Zeta function; Psi (or Digamma) function; Bernoulli numbers; Bohr-Mollerup theorem; Euler-Mascheroni and Glaisher-Kinkelin constant; Determinants of the La
Mathieu series and associated sums involving the Zeta functions
Keywords: اعداد برنولی; Euler–Mascheroni constant; Gamma function; Psi (or Digamma) function; Trigamma and Polygamma functions; Riemann Zeta function; Hurwitz (or generalized) Zeta function; Dirichlet Eta function; Bernoulli numbers; Mathieu series; Alternating Mathieu series; F
A unified presentation of identities involving Weierstrass-type functions and their applications
Keywords: اعداد برنولی; Bernoulli numbers; Weierstrass ℘℘-function; Weierstrass-type functions; Euler’s identity; Zeta function; Eisenstein series
On the behaviour of p-adic L-functions
Keywords: اعداد برنولی; primary, 11R23, 11S40; secondary, 11B68Iwasawa λ-invariants; p-Adic L-functions; Bernoulli numbers
Complete monotonicity of some functions involving polygamma functions
Keywords: اعداد برنولی; 26A48; 26A51; 26D20; 33B10; 33B15; 44A10Monotonicity; Completely monotonic function; Polygamma function; Infinite series; Bernoulli numbers
Padé approximation and Apostol–Bernoulli and Apostol–Euler polynomials
Keywords: اعداد برنولی; 11B68; 41A21Apostol–Bernoulli polynomials; Apostol–Euler polynomials; Bernoulli numbers; Euler numbers; Padé approximants
New congruences for central binomial coefficients
Keywords: اعداد برنولی; primary, 11B65; secondary, 05A10, 05A19, 11A07, 11B39, 11B68Central binomial coefficients; Congruences modulo primes; Fibonacci numbers; Bernoulli numbers
Some discrete Fourier transform pairs associated with the Lipschitz–Lerch Zeta function
Keywords: اعداد برنولی; Hurwitz–Lerch Zeta function; Lipschitz–Lerch Zeta function; Lerch Zeta function; Hurwitz Zeta function; Riemann Zeta function; Legendre chi function; Bernoulli polynomials; Bernoulli numbers; Discrete Fourier transform
Values of the derivatives of the cotangent at rational multiples of π
Keywords: اعداد برنولی; Cotangent function; Simpson’s series multisection formula; Bernoulli polynomials; Bernoulli numbers; Hurwitz zeta function; Polylogarithm
Computation of Euler’s type sums of the products of Bernoulli numbers
Keywords: اعداد برنولی; Bernoulli numbers; Bernoulli polynomials; Sums of products; Euler’s sums; Dilcher’s sums; Multinomial coefficients; Integer sequences; Generating functions; Cauchy product of power series; Stirling numbers of the first kind
Sharpening Redheffer-type inequalities for circular functions
Keywords: اعداد برنولی; Sharpening Redheffer-type inequalities; Circular functions; Upper and lower bounds; Bernoulli numbers; The Riemann’s zeta function
Summation formulae for finite cotangent sums
Keywords: اعداد برنولی; Trigonometric sums; Finite summation; Cotangent sums; Alternate cotangent sums; Contour integration; Cauchy residue theorem; Higher order Bernoulli polynomials; Bernoulli polynomials; Bernoulli numbers
Note on some congruences of Lehmer
Keywords: اعداد برنولی; primary, 11A07; secondary, 11B68Lehmer's congruences; Euler's totient function; Bernoulli numbers
On a pp-adic interpolation function for the qq-extension of the generalized Bernoulli polynomials and its derivative
Keywords: اعداد برنولی; pp-adic qq-integrals; pp-adic LL-function; Bernoulli numbers