zeros of cylinder functions

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1: 12.11 Zeros

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§12.11(i) Distribution of Real Zeros

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§12.11(ii) Asymptotic Expansions of Large Zeros

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§12.11(iii) Asymptotic Expansions for Large Parameter

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2: 10.1 Special Notation

… ►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).

3: 10.21 Zeros

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§10.21(i) Distribution

… ►If ${\sigma }_{\nu }$ is a zero of ${𝒞}_{\nu }^{\prime }\left(z\right)$, then … ► … ►

§10.21(iv) Monotonicity Properties

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4: 12.14 The Function $W(a,x)$

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§12.14(xi) Zeros of $W(a,x)$, $W^{\prime }(a,x)$

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5: Bibliography D

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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).

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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6: Bibliography S

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A global Newton method for the zeros of cylinder functions. Numer. Algorithms 18 (3-4), pp. 259–276.

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External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

BibTeX

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7: Bibliography M

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Some remarks on zeros of cylinder functions. SIAM J. Math. Anal. 15 (6), pp. 1231–1233.

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External Links:

ISSN 0036-1410, Document, FullText, MathReview (A. K. Agarwal), ZentralBlatt

Referenced by:

§10.14, §10.21(ii).

Encodings:

BibTeX

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8: 18.24 Hahn Class: Asymptotic Approximations

… ►This expansion is in terms of the parabolic cylinder function and its derivative. … ►Asymptotic approximations are also provided for the zeros of $K_n(x;p,N)$ in various cases depending on the values of $p$ and $\mu$. … ►Both expansions are in terms of parabolic cylinder functions. ►For asymptotic approximations for the zeros of $M_n(nx;\beta ,c)$ in terms of zeros of $\mathrm{Ai}\left(x\right)$ (§9.9(i)), see Jin and Wong (1999) and Khwaja and Olde Daalhuis (2012). … ►This expansion is uniformly valid in any compact $x$-interval on the real line and is in terms of parabolic cylinder functions. …

9: Bibliography N

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Proofs of two conjectures on the real zeros of the cylinder and Airy functions. SIAM J. Math. Anal. 53 (4), pp. 4328–4349.

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External Links:

ISSN 0036-1410, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(10.18.17), (10.18.18), §10.18(iii), (9.8.22), (9.8.23), §9.8(iv), Erratum (V1.1.8) for Section 9.8(iv), Erratum (V1.1.8) for Section 10.18(iii).

Encodings:

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10: 32.10 Special Function Solutions

… ►When $a+\frac{1}{2}$ is zero or a negative integer the $U$ parabolic cylinder functions reduce to Hermite polynomials (§18.3) times an exponential function; thus …