Nörlund polynomials

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11: 24.17 Mathematical Applications

§24.17 Mathematical Applications

… ►See Milne-Thomson (1933), Nörlund (1924), or Jordan (1965). … ►

§24.17(iii) Number Theory

►Bernoulli and Euler numbers and polynomials occur in: number theory via (24.4.7), (24.4.8), and other identities involving sums of powers; the Riemann zeta function and $L$-series (§25.15, Apostol (1976), and Ireland and Rosen (1990)); arithmetic of cyclotomic fields and the classical theory of Fermat’s last theorem (Ribenboim (1979) and Washington (1997)); $p$-adic analysis (Koblitz (1984, Chapter 2)).

12: 16.8 Differential Equations

… ►For details see Smith (1939a, b), and Nørlund (1955). … ►(Note that the generalized hypergeometric functions on the right-hand side are polynomials in $z_0$.) … ►For details see Nørlund (1955). …

13: Bibliography N

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Orthogonal polynomials. Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..

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External Links:

ISSN 0065-9266, Document, Link, MathReview (T. S. Chihara)

Referenced by:

§18.2(xi), §18.2(xi).

Encodings:

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Hypergeometric functions. Acta Math. 94, pp. 289–349.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§16.10, §16.8(ii), §16.8(ii).

Encodings:

BibTeX

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Mémoire sur les polynomes de Bernoulli. Acta Math. 43, pp. 121–196 (French).

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External Links:

Document, ZentralBlatt

Referenced by:

§24.13(i), §24.13(ii), §24.14(i), Ch.24.

Encodings:

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Vorlesungen über Differenzenrechnung. Springer-Verlag, Berlin (German).

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Notes:

Reprinted 1954 by Chelsea Publishing Company, New York

External Links:

ZentralBlatt

Referenced by:

§24.1, §24.1, §24.13(i), §24.13(ii), §24.16(i), §24.17(i), §24.17(i), §24.2(i), §24.2(ii), §24.4(i), §24.4(ii), §24.4(iii), §24.4(v), §24.5(i), Ch.24, (25.6.6).

Encodings:

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Askey-Wilson polynomials: an affine Hecke algebra approach. In Laredo Lectures on Orthogonal Polynomials and Special Functions, Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.

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External Links:

MathReview (V. L. Deshpande), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

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