zeros%20of%20polynomials

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1: Bibliography L

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Inequalities and approximations for zeros of Bessel functions of small order. SIAM J. Math. Anal. 14 (2), pp. 383–388.

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ISSN 0036-1410, Document, MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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The real zeros of the Bernoulli polynomials. J. Approx. Theory 58 (2), pp. 124–150.

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ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§24.12(i), §24.9.

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On the asymptotics of the Meixner-Pollaczek polynomials and their zeros. Constr. Approx. 17 (1), pp. 59–90.

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ISSN 0176-4276, Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§18.24.

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2: 3.8 Nonlinear Equations

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§3.8(iv) Zeros of Polynomials

… ►In this way polynomials of successively lower degree can be used to find the remaining zeros. … ►

Bairstow’s Method

… ►For further information on the computation of zeros of polynomials see McNamee (2007). … ►

§3.8(vi) Conditioning of Zeros

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3: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

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On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

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ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

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

Referenced by:

§31.15(ii).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

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4: Bibliography D

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On the zeros of generalized Bessel polynomials. I. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.

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ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

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On the zeros of generalized Bessel polynomials. II. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.

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ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

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Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Mem. Amer. Math. Soc. 73 (386), pp. iv+94.

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ISSN 0065-9266, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i), §24.12(iii), §24.16(ii).

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On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

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ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.12(iv).

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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Notes:

For a numerical error in one of the zeros see Amos (1985).

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

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5: Bibliography V

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On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp. 46 (174), pp. 667–681.

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ISSN 0025-5718, FullText, Document, MathReview (Jürgen G. Hinz), ZentralBlatt

Referenced by:

§25.10(ii), §25.18(ii).

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials. J. Comput. Appl. Math. 213 (2), pp. 488–500.

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ISSN 0377-0427, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

item (f), §28.34(ii), §29.20(i).

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On the localization and computation of zeros of Bessel functions. Z. Angew. Math. Mech. 77 (6), pp. 467–475.

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ISSN 0044-2267, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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The topological degree theory for the localization and computation of complex zeros of Bessel functions. Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.

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ISSN 0163-0563, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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6: Bibliography S

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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.

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ISSN 0025-5718, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.74(vi).

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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

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

Referenced by:

§18.2(xii).

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A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

External Links:

Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

Referenced by:

3rd item.

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7: Bibliography M

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

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Inequalities for the zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 166–170.

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ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.21(iv).

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.

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FullText

Referenced by:

§8.24(i).

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

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8: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

Referenced by:

1st item, 4th item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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

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

Referenced by:

§18.35(iii).

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9: Bibliography C

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Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial $L_n^{\alpha }(x)$ as the index $\alpha \to \mathrm{\infty }$ and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.

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ISSN 0024-1318, Document, MathReview (R. A. Askey)

Referenced by:

§18.7(iii).

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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Asymptotics of the largest zeros of some orthogonal polynomials. J. Phys. A 31 (25), pp. 5525–5544.

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ISSN 0305-4470, Document, MathReview (Tim H. Baker), ZentralBlatt

Referenced by:

§18.26(v), §18.29.

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On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.

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ISSN 0036-1410, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.38(iii).

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

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10: Bibliography P

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Interlacing of positive real zeros of Bessel functions. J. Math. Anal. Appl. 375 (1), pp. 320–322.

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ISSN 0022-247X, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§10.21(i), §10.21(i).

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Complex zeros of the modified Bessel function $K_n(Z)$ . Math. Comp. 26 (120), pp. 949–953.

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

1st item.

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

Referenced by:

6th item.

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Chebyshev series approximations for the zeros of the Bessel functions. J. Comput. Phys. 53 (1), pp. 188–192.

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ISSN 0021-9991, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.76(ii).

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On the computation of zeros and turning points of Bessel functions. Bull. Soc. Math. Grèce (N.S.) 31, pp. 117–122.

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External Links:

MathReview (Alan M. Cohen), ZentralBlatt

Referenced by:

§10.76(ii).

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