zeros of polynomials

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31: Bibliography B

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Asymptotic behavior of the Pollaczek polynomials and their zeros. Stud. Appl. Math. 96, pp. 307–338.

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External Links:

ISSN 0022-2526, MathReview (Harold Exton), ZentralBlatt

Referenced by:

§18.35(iii).

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32: 18.41 Tables

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§18.41(i) Polynomials

►For $P_n\left(x\right)$ ($={𝖯}_n\left(x\right)$) see §14.33. ►Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates $T_n\left(x\right)$, $U_n\left(x\right)$, $L_n\left(x\right)$, and $H_n\left(x\right)$ for $n=0(1)12$. The ranges of $x$ are $0.2(.2)1$ for $T_n\left(x\right)$ and $U_n\left(x\right)$, and $0.5,1,3,5,10$ for $L_n\left(x\right)$ and $H_n\left(x\right)$. … ►

§18.41(ii) Zeros

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33: Bibliography

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Zeros of Stieltjes and Van Vleck polynomials and applications. J. Math. Anal. Appl. 110 (2), pp. 327–339.

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ISSN 0022-247X, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§31.15(ii).

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Zeros of Stieltjes and Van Vleck polynomials. Trans. Amer. Math. Soc. 252, pp. 197–204.

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External Links:

ISSN 0002-9947, FullText, MathReview (Pet”r Rusev), ZentralBlatt

Referenced by:

§31.15(ii).

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34: Bibliography K

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Zeros of exceptional Hermite polynomials. J. Approx. Theory 200, pp. 28–39.

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External Links:

ISSN 0021-9045, Document, Link, MathReview (Mario Pérez Riera)

Referenced by:

§18.39(i).

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35: Bibliography E

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Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comput. Appl. Math. 133 (1-2), pp. 65–83.

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External Links:

ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.21(iv).

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36: Bibliography R

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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External Links:

ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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External Links:

ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

Encodings:

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37: 15.13 Zeros

§15.13 Zeros

►Let $N(a,b,c)$ denote the number of zeros of $F(a,b;c;z)$ in the sector . If $a$, $b$, $c$ are real, $a$, $b$, $c$, $c-a$, $c-b\ne 0,-1,-2,\mathrm{\dots }$, and, without loss of generality, $b\ge a$, $c\ge a+b$ (compare (15.8.1)), then … ►For further information on the location of real zeros see Zarzo et al. (1995) and Dominici et al. (2013). A small table of zeros is given in Conde and Kalla (1981) and Segura (2008).

38: Bibliography S

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Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.

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External Links:

ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.2(xii).

Encodings:

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39: 19.14 Reduction of General Elliptic Integrals

… ►The choice among 21 transformations for final reduction to Legendre’s normal form depends on inequalities involving the limits of integration and the zeros of the cubic or quartic polynomial. …

40: 18.17 Integrals

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Jacobi

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Laguerre

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Ultraspherical

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Legendre

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Hermite

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