Stirling polynomials
In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling polynomial sequence considered below most notably including the Sheffer sequence form of the sequence, , defined characteristically through the special form of its exponential generating function, and the Stirling (convolution) polynomials, , which also satisfy a characteristic ordinary generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "convolution polynomial" variant of this sequence
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Bernoulli numberBernoulli polynomialsBernoulli polynomials of the second kindDouble factorialGenerating functionGregory coefficientsMittag-Leffler polynomialsPochhammer k-symbolPoly-Bernoulli numberStirling numbers of the first kindStirling numbers of the second kindStirling polynomialStirling polynomials
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Stirling polynomials
In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling polynomial sequence considered below most notably including the Sheffer sequence form of the sequence, , defined characteristically through the special form of its exponential generating function, and the Stirling (convolution) polynomials, , which also satisfy a characteristic ordinary generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "convolution polynomial" variant of this sequence
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In mathematics, the Stirling p ...... icles given in the references.
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Nørlund Polynomial
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Stirling Polynomial
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Stirling polynomial
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NorlundPolynomial
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StirlingPolynomial
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In mathematics, the Stirling p ...... mial" variant of this sequence
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Stirling polynomials
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