Mathematical Inequalities and Applications, ISSN 1331-4343, 07/2016, Volume 19, Issue 3, pp. 841 - 851

In this paper, we presented the Raabe's integral and Hermite's formula for q-gamma function Gamma(q)(x), 0 < q < 1. We deduced new proofs of the formulas...

Raabe's integral | Q-gamma function | Functional equations | Hermite's formula | Q-Gauss's multiplication | Inequality | MATHEMATICS | inequality | functional equations | q-Gauss's multiplication | q-gamma function

Raabe's integral | Q-gamma function | Functional equations | Hermite's formula | Q-Gauss's multiplication | Inequality | MATHEMATICS | inequality | functional equations | q-Gauss's multiplication | q-gamma function

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 05/2009, Volume 20, Issue 5, pp. 377 - 391

This article obtains the multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order and deduces some explicit recursive...

Euler numbers and polynomials (of higher order) | multiplication formula | Primary: 11B68 | Bernoulli numbers and polynomials (of higher order) | Raabe's multiplication formula | λ-multiple power sum and λ-multiple alternating sum | Secondary: 05A10 | generalized multinomial identity | power sum and alternating sum | Apostol-Euler numbers and polynomials (of higher order) | multinomial identity | Apostol-Bernoulli numbers and polynomials (of higher order) | Generalized multinomial identity | Multiplication formula | Multinomial identity | Power sum and alternating sum | MATHEMATICS, APPLIED | NUMBERS | MATHEMATICS | multiple power sum and -multiple alternating sum

Euler numbers and polynomials (of higher order) | multiplication formula | Primary: 11B68 | Bernoulli numbers and polynomials (of higher order) | Raabe's multiplication formula | λ-multiple power sum and λ-multiple alternating sum | Secondary: 05A10 | generalized multinomial identity | power sum and alternating sum | Apostol-Euler numbers and polynomials (of higher order) | multinomial identity | Apostol-Bernoulli numbers and polynomials (of higher order) | Generalized multinomial identity | Multiplication formula | Multinomial identity | Power sum and alternating sum | MATHEMATICS, APPLIED | NUMBERS | MATHEMATICS | multiple power sum and -multiple alternating sum

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2013, Volume 36, Issue 2, pp. 465 - 479

The present paper deals with multiplication formulas for the Apostol-Genocchi polynomials of higher order and deduces some explicit recursive formulas. Some...

Raabe's multiplication formula | Euler numbers and polynomials | Bernoulli numbers and polynomials | Multiplication formula | Stirling numbers | Apostol-Genocchi numbers and polynomials (of higher order) | Generalization of Genocchi numbers and polynomials | BERNOULLI NUMBERS | generalization of Genocchi numbers and polynomials | MATHEMATICS | multiplication formula | ZETA | EULER POLYNOMIALS | EXPLICIT FORMULAS | Q-EXTENSION

Raabe's multiplication formula | Euler numbers and polynomials | Bernoulli numbers and polynomials | Multiplication formula | Stirling numbers | Apostol-Genocchi numbers and polynomials (of higher order) | Generalization of Genocchi numbers and polynomials | BERNOULLI NUMBERS | generalization of Genocchi numbers and polynomials | MATHEMATICS | multiplication formula | ZETA | EULER POLYNOMIALS | EXPLICIT FORMULAS | Q-EXTENSION

Journal Article

Mathematical Notes, ISSN 0001-4346, 2/2012, Volume 91, Issue 1, pp. 46 - 57

We investigate multiplication formulas for Apostol-type polynomials and introduce λ-multiple alternating sums, which are evaluated by Apostol-type polynomials....

Apostol-Bernoulli numbers and polynomials | recursive formula | λ-multiple alternating sum | Apostol-type polynomials | Raabe’s multiplication formula | alternating sum | Apostol-Euler numbers and polynomials | Mathematics, general | Mathematics | generalized multinomial identity | Apostol-Genocchi numbers and polynomials | multinomial identity | Raabe's multiplication formula | MATHEMATICS | BERNOULLI | lambda-multiple alternating sum

Apostol-Bernoulli numbers and polynomials | recursive formula | λ-multiple alternating sum | Apostol-type polynomials | Raabe’s multiplication formula | alternating sum | Apostol-Euler numbers and polynomials | Mathematics, general | Mathematics | generalized multinomial identity | Apostol-Genocchi numbers and polynomials | multinomial identity | Raabe's multiplication formula | MATHEMATICS | BERNOULLI | lambda-multiple alternating sum

Journal Article

Kyushu Journal of Mathematics, ISSN 1340-6116, 2008, Volume 62, Issue 1, pp. 171 - 187

Deformations of the multiple gamma and sine functions with respect to their periods are studied. To describe such deformations explicitly, a new class of...

multiple gamma function; multiple sine | Raabe's formula | multiple Hurwitz's zeta function | multiplication formulas | function | Multiple sine function | Multiple Hurwitz's zeta function | Multiple gamma function | Multiplication formulas | MATHEMATICS | ZETA-FUNCTION | multiple gamma function | multiple sine function

multiple gamma function; multiple sine | Raabe's formula | multiple Hurwitz's zeta function | multiplication formulas | function | Multiple sine function | Multiple Hurwitz's zeta function | Multiple gamma function | Multiplication formulas | MATHEMATICS | ZETA-FUNCTION | multiple gamma function | multiple sine function

Journal Article

Utilitas Mathematica, ISSN 0315-3681, 11/2014, Volume 95, pp. 85 - 95

We show the basic properties and generating functions of the q-Apostol-Bernoulli polynomials. Some recursive formulas are derived in series of the q-power...

Q-Hurwitz-Lerch zeta function | Apostol-bernoulli polynomials and numbers | Q-apostol-bernoulli polynomials and numbers | Power sums and q-power sums | Q-raabe's multiplication theorem | q-Apostol-Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | HIGHER-ORDER | NUMBERS | EULER POLYNOMIALS | EXPANSIONS | Apostol-Bernoulli polynomials and numbers | q-Raabe's multiplication theorem | power sums and q-power sums | STATISTICS & PROBABILITY | q-Hurwitz-Lerch zeta function

Q-Hurwitz-Lerch zeta function | Apostol-bernoulli polynomials and numbers | Q-apostol-bernoulli polynomials and numbers | Power sums and q-power sums | Q-raabe's multiplication theorem | q-Apostol-Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | HIGHER-ORDER | NUMBERS | EULER POLYNOMIALS | EXPANSIONS | Apostol-Bernoulli polynomials and numbers | q-Raabe's multiplication theorem | power sums and q-power sums | STATISTICS & PROBABILITY | q-Hurwitz-Lerch zeta function

Journal Article

Research in Number Theory, ISSN 2363-9555, 12/2017, Volume 3, Issue 1, pp. 1 - 12

We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of...

Primary 11P81 | Sylvester waves | Raabe’s identity | Mathematics | Restricted partitions | Bernoulli polynomials | Number Theory | Secondary 11B68 | Probability | Research

Primary 11P81 | Sylvester waves | Raabe’s identity | Mathematics | Restricted partitions | Bernoulli polynomials | Number Theory | Secondary 11B68 | Probability | Research

Journal Article

Applicable Analysis: Approximation Theory and Signal Analysis, a special issue in honour of Professor Paul Leo Butzer, ISSN 0003-6811, 03/2011, Volume 90, Issue 3-4, pp. 643 - 688

This article discusses the interplay between multiplex signal transmission in telegraphy and telephony, and sampling methods. It emphasizes the works of...

Raabe's condition | multiplexing | 01-02 | sampling theorem | historical review | Nyquist rate | Shannon theory | 94-03 | MATHEMATICS, APPLIED | MATHEMATICAL-ANALYSIS | THEOREM | ORIGINS | RANDOM NOISE | INFORMATION-THEORY | SYSTEMS | COMMUNICATION | Multiplexing | Construction | Mathematical analysis | Prototypes | Construction equipment | Telephony | Band theory | Signal transmission | Sampling

Raabe's condition | multiplexing | 01-02 | sampling theorem | historical review | Nyquist rate | Shannon theory | 94-03 | MATHEMATICS, APPLIED | MATHEMATICAL-ANALYSIS | THEOREM | ORIGINS | RANDOM NOISE | INFORMATION-THEORY | SYSTEMS | COMMUNICATION | Multiplexing | Construction | Mathematical analysis | Prototypes | Construction equipment | Telephony | Band theory | Signal transmission | Sampling

Journal Article

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