Polynomials: Special Polynomials and Number-Theoretical Applications
Pintér, Ákos
Polynomials: Special Polynomials and Number-Theoretical Applications - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (154 p.)
Open Access
Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well
Creative Commons
English
books978-3-0365-0819-1 9783036508184 9783036508191
10.3390/books978-3-0365-0819-1 doi
Research & information: general
Mathematics & science
Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method
Polynomials: Special Polynomials and Number-Theoretical Applications - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021 - 1 electronic resource (154 p.)
Open Access
Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well
Creative Commons
English
books978-3-0365-0819-1 9783036508184 9783036508191
10.3390/books978-3-0365-0819-1 doi
Research & information: general
Mathematics & science
Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method