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15 relations: Appell sequence, Boas–Buck polynomials, Brenke–Chihara polynomials, Degree of a polynomial, Difference polynomials, Generating function, Kernel (category theory), Mathematics, Newton polynomial, Partition (number theory), Polynomial, Polynomial sequence, Q-difference polynomial, Recurrence relation, Sheffer sequence.
Appell sequence
In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence \_ satisfying the identity and in which p_0(x) is a non-zero constant.
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Boas–Buck polynomials
In mathematics, Boas–Buck polynomials are sequences of polynomials Φ(x) given by generating functions of the form The case r.
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Brenke–Chihara polynomials
In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and Brenke–Chihara polynomials are the Brenke polynomials that are also orthogonal polynomials.
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Degree of a polynomial
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
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Difference polynomials
In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selberg's polynomials, and the Stirling interpolation polynomials as special cases.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Kernel (category theory)
In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points.
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Partition (number theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Polynomial sequence
In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3,..., in which each index is equal to the degree of the corresponding polynomial.
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Q-difference polynomial
In combinatorial mathematics, the q-difference polynomials or q-harmonic polynomials are a polynomial sequence defined in terms of the ''q''-derivative.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Sheffer sequence
In mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence of polynomials in which the index of each polynomial equals its degree, satisfying conditions related to the umbral calculus in combinatorics.
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Generalized Appell representation, Generalized Appell sequence, Generalized appell polynomials.
References
[1] https://en.wikipedia.org/wiki/Generalized_Appell_polynomials
