On polynomials related to powers of the generating function of Catalan's numbers. (Q2707838)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On polynomials related to powers of the generating function of Catalan's numbers. |
scientific article |
Statements
4 April 2001
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Catalan numbers
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On polynomials related to powers of the generating function of Catalan's numbers. (English)
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If the integer \(n\geq 0\), the \(n\)th Catalan number may be defined by: NEWLINE\[NEWLINEC_n= {1\over n+1} {2n\choose n}.NEWLINE\]NEWLINE (The above identity is not mentioned in the article.) The author is chiefly concerned with obtaining results concerning the associated generating function: NEWLINE\[NEWLINEc(x)= \sum^\infty_{n=0} C_n x^n.NEWLINE\]NEWLINE For example, he obtains a formula for \(c^n(x)\) (the \(n\)th power of \(c(x)\)) in terms of \(c(x)\) and a function related to Chebyshev polynomials of the second kind.
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