of zeros

SearchAdvancedHelp

(0.001 seconds)

21—30 of 185 matching pages

21: 13.9 Zeros

§13.9 Zeros

►

§13.9(i) Zeros of $M(a,b,z)$

… ► … ► … ► …

22: 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).

23: 12.11 Zeros

§12.11 Zeros

►

§12.11(i) Distribution of Real Zeros

… ►

§12.11(ii) Asymptotic Expansions of Large Zeros

… ►

§12.11(iii) Asymptotic Expansions for Large Parameter

… ►For the first zero of $U(a,x)$ we also have …

24: 3.8 Nonlinear Equations

… ►

§3.8(iv) Zeros of Polynomials

… ►has $n$ zeros in $ℂ$, counting each zero according to its multiplicity. … ►

§3.8(v) Zeros of Analytic Functions

… ►

§3.8(vi) Conditioning of Zeros

… ►The zeros of …

25: 18.16 Zeros

§18.16 Zeros

… ►

§18.16(ii) Jacobi

… ►

Inequalities

… ►

§18.16(iii) Ultraspherical, Legendre and Chebyshev

… ►

§18.16(iv) Laguerre

…

26: 4.46 Tables

… ►This handbook also includes lists of references for earlier tables, as do Fletcher et al. (1962) and Lebedev and Fedorova (1960). … ►(These roots are zeros of the Bessel function $J_{3/2}\left(x\right)$; see §10.21.) …

27: 29.20 Methods of Computation

… ►A fourth method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree. … ►

§29.20(iii) Zeros

►Zeros of Lamé polynomials can be computed by solving the system of equations (29.12.13) by employing Newton’s method; see §3.8(ii). Alternatively, the zeros can be found by locating the maximum of function $g$ in (29.12.11).

28: 9.18 Tables

… ►

§9.18(iv) Zeros

►

Miller (1946) tabulates $a_k$, ${\mathrm{Ai}}^{\prime }\left(a_k\right)$, $a_k^{\prime }$, $\mathrm{Ai}\left(a_k^{\prime }\right)$, $k=1(1)50$; $b_k$, ${\mathrm{Bi}}^{\prime }\left(b_k\right)$, $b_k^{\prime }$, $\mathrm{Bi}\left(b_k^{\prime }\right)$, $k=1(1)20$. Precision is 8D. Entries for $k=1(1)20$ are reproduced in Abramowitz and Stegun (1964, Chapter 10).

►

Sherry (1959) tabulates $a_k$, ${\mathrm{Ai}}^{\prime }\left(a_k\right)$, $a_k^{\prime }$, $\mathrm{Ai}\left(a_k^{\prime }\right)$, $k=1(1)50$; 20S.

►

Zhang and Jin (1996, p. 339) tabulates $a_k$, ${\mathrm{Ai}}^{\prime }\left(a_k\right)$, $a_k^{\prime }$, $\mathrm{Ai}\left(a_k^{\prime }\right)$, $b_k$, ${\mathrm{Bi}}^{\prime }\left(b_k\right)$, $b_k^{\prime }$, $\mathrm{Bi}\left(b_k^{\prime }\right)$, $k=1(1)20$; 8D.

… ►

Gil et al. (2003c) tabulates the only positive zero of ${\mathrm{Gi}}^{\prime }\left(z\right)$, the first 10 negative real zeros of $\mathrm{Gi}\left(z\right)$ and ${\mathrm{Gi}}^{\prime }\left(z\right)$, and the first 10 complex zeros of $\mathrm{Gi}\left(z\right)$, ${\mathrm{Gi}}^{\prime }\left(z\right)$, $\mathrm{Hi}\left(z\right)$, and ${\mathrm{Hi}}^{\prime }\left(z\right)$. Precision is 11 or 12S.

…

29: 14.16 Zeros

§14.16 Zeros

… ►

§14.16(ii) Interval

… ►

§14.16(iii) Interval

► $P_{\nu }^{\mu }\left(x\right)$ has exactly one zero in the interval $(1,\mathrm{\infty })$ if either of the following sets of conditions holds: … ► ${𝑸}_{\nu }^{\mu }\left(x\right)$ has no zeros in the interval $(1,\mathrm{\infty })$ when $\nu >-1$, and at most one zero in the interval $(1,\mathrm{\infty })$ when .

30: Bibliography Q

… ►

Asymptotic expansion of the Krawtchouk polynomials and their zeros. Comput. Methods Funct. Theory 4 (1), pp. 189–226.

ⓘ

External Links:

ISSN 1617-9447, FullText, MathReview (C. M. Joshi), ZentralBlatt (N. M. Temme)

Referenced by:

§18.24.

Encodings:

BibTeX

►

“Best possible” upper and lower bounds for the zeros of the Bessel function $J_{\nu }(x)$ . Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.

ⓘ

External Links:

ISSN 0002-9947, FullText, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(vii).

Encodings:

BibTeX

…