Some identities involving exponential functions and Stirling numbers and applications

“…For saving time of the authors and space of this paper, we do not write down them in details. Due to the same motivation and reason as Theorem 3.1, the authors composed and published the papers [10,11,21,30,31,40,41,42,43,44,47,55,56,57,58,66,67,70], for examples.…”

Section: Remarksmentioning

confidence: 99%

Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers

Qi¹,

Zou²,

Guo³

2017

Preprint

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Abstract. In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, acquire a binomial inversion formula, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials of the second kind, the central Delannoy numbers, and the Fibonacci polynomials.

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“…For saving time of the authors and space of this paper, we do not write down them in details. Due to the same motivation and reason as Theorem 3.1, the authors composed and published the papers [10,19,20,21,35,36,37,38,48,49,50,57,58], for examples. Actually, the identity (5.3) is a special case i = j ∈ N of the identity (5.1).…”

Section: Remarksmentioning

confidence: 99%

Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers

Qi¹,

Guo²

2017

Preprint

View full text Add to dashboard Cite

Abstract. In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

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Some identities involving exponential functions and Stirling numbers and applications

Cited by 32 publications

References 11 publications

Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers

Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers

Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers

Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers

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