interlacing

SearchAdvancedHelp

(0.001 seconds)

10 matching pages

1: 14.16 Zeros

… ►The zeros of ${𝖰}_{\nu }^{\mu }\left(x\right)$ in the interval $(-1,1)$ interlace those of ${𝖯}_{\nu }^{\mu }\left(x\right)$. …

2: Bibliography E

… ►

Interlacing properties of the zeros of Bessel functions. Atti Sem. Mat. Fis. Univ. Modena XLII (2), pp. 525–529.

ⓘ

External Links:

ISSN 0041-8986, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.21(i).

Encodings:

BibTeX

…

3: 29.3 Definitions and Basic Properties

… ►

§29.3(ii) Distribution

►The eigenvalues interlace according to …

4: Bibliography P

… ►

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

ⓘ

External Links:

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

Referenced by:

§10.21(i), §10.21(i).

Encodings:

BibTeX

…

5: 28.29 Definitions and Basic Properties

… ►Both ${\lambda }_n$ and ${\mu }_n\to \mathrm{\infty }$ as $n\to \mathrm{\infty }$, and interlace according to the inequalities …

6: 10.21 Zeros

… ►When $\nu \ge 0$, the zeros interlace according to the inequalities … ►

10.21.3

ⓘ

Symbols:

$j_{\nu ,m}$: zeros of the Bessel function $J_{\nu }\left(x\right)$ , $y_{\nu ,m}$: zeros of the Bessel function $Y_{\nu }\left(x\right)$ , $j_{\nu ,m}^{\prime }$: zeros of the Bessel function derivative $J_{\nu }^{\prime }\left(x\right)$ , $y_{\nu ,m}^{\prime }$: zeros of the Bessel function derivative $Y_{\nu }^{\prime }\left(x\right)$ and $\nu$: complex parameter

A&S Ref:

9.5.2

Referenced by:

§10.21(ii)

Permalink:

http://dlmf.nist.gov/10.21.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §10.21(i), §10.21 and Ch.10

… ►The positive zeros of any two real distinct cylinder functions of the same order are interlaced, as are the positive zeros of any real cylinder function ${𝒞}_{\nu }\left(z\right)$ and the contiguous function ${𝒞}_{\nu +1}\left(z\right)$. …

7: 10.18 Modulus and Phase Functions

…

8: Bibliography S

… ►

Interlacing of the zeros of contiguous hypergeometric functions. Numer. Algorithms 49 (1-4), pp. 387–407.

ⓘ

External Links:

ISSN 1017-1398, Document, FullText, MathReview, ZentralBlatt

Referenced by:

§13.9(i), §13.9(i), §13.9(ii), §13.9(ii), §15.13, §15.13.

Encodings:

BibTeX

…

9: 9.12 Scorer Functions

… ►Both $\mathrm{Gi}\left(z\right)$ and ${\mathrm{Gi}}^{\prime }\left(z\right)$ have an infinity of negative real zeros, and they are interlaced. …

10: 19.29 Reduction of General Elliptic Integrals

… ►(The variables of $R_F$ are real and nonnegative unless both $Q$’s have real zeros and those of $Q_1$ interlace those of $Q_2$.) …