We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials ins...

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed.

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other belongs to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.

We study generating functions for the number of even (odd) permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations in Sn subject to set of restrictions. One of the restrictions belongs to S3, while the others to Sk. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind. 2001 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70 42C05

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

We study generating functions for the number of permutations in S n subject to two restrictions. One of the restrictions belongs to S 3 , while the other belongs to S k. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.