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1: Bibliography W

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Shadows cast on the bottom of a pool are not like other shadows. Why?. Scientific American 259, pp. 86–89.

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Referenced by:

§36.14(ii).

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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External Links:

ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

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Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

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ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

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Asymptotic expansions for second-order linear difference equations. II. Stud. Appl. Math. 87 (4), pp. 289–324.

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ISSN 0022-2526, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(ii).

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Asymptotic expansions for second-order linear difference equations. J. Comput. Appl. Math. 41 (1-2), pp. 65–94.

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ISSN 0377-0427, Document, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(i), §2.9(ii).

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2: Wadim Zudilin

… ►He has been an Associate Professor at Moscow State University (Russia), an Ostrowski Fellow at Institut Henri Poincaré and Université Paris 6 (France), a Humboldt Fellow at the Cologne University (Germany) and a Visiting Researcher at the Max Planck Institute for Mathematics in Bonn (Germany). His research interests are primarily focused on applications of special functions in different parts of number theory. …

3: Bibliography L

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Functions on a parabolic cylinder with a negative integer index. Differ. Uravn. 21 (11), pp. 2001–2003, 2024 (Russian).

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Notes:

In Russian.

External Links:

ISSN 0374-0641, MathReview, ZentralBlatt

Referenced by:

§12.13(i).

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Introduction to spectral theory: selfadjoint ordinary differential operators. Translations of Mathematical Monographs, Vol. 39, American Mathematical Society, Providence, R.I..

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Notes:

Translated from the Russian by Amiel Feinstein

External Links:

MathReview Entry

Referenced by:

§1.18(x).

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Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

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ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

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Numerical Solution of Linear Difference Equations. NBSIR Technical Report 80-1976, National Bureau of Standards, Gaithersburg, MD 20899.

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Notes:

(Available from National Technical Information Service, Springfield, VA 22161.)

Referenced by:

§16.25, §3.6(vii).

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The second Painlevé equation. Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).

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Notes:

In Russian. English translation: Differential Equations 7(6), pp. 853–854

External Links:

MathReview (Z. Rubinstein), ZentralBlatt

Referenced by:

§32.7(ii).

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4: 19.29 Reduction of General Elliptic Integrals

… ►(This shows why $I({𝐞}_{\alpha })$ is not needed as a basic integral in the cubic case.) …

5: 28.27 Addition Theorems

… ►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …

6: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For $T$ to be actually self adjoint it is necessary to also show that $𝒟(T^{\ast })=𝒟(T)$, as it is often the case that $T$ and $T^{\ast }$ have different domains, see Friedman (1990, p 148) for a simple example of such differences involving the differential operator $\frac{d}{dx}$. … ►This work is well overviewed by Coddington and Levinson (1955, Ch. 9), and then applied in detail by Titchmarsh (1946), Titchmarsh (1962a), Titchmarsh (1958), and Levitan and Sargsjan (1975) which also connects the Weyl theory to the relevant functional analysis. …

7: Charles W. Clark

… ►He has been a Visiting Fellow at the Australian National University, a Dr. Lee Fellow at Christ Church College of the University of Oxford, and Visiting Professor at the National University of Singapore. …

8: 3.6 Linear Difference Equations

§3.6 Linear Difference Equations

… ► … ► … ►The difference equation … …

9: Leonard C. Maximon

… ►He had been an Assistant Professor in the Graduate Division of Applied Mathematics at Brown University, a Visiting Professor at the Norwegian Technical University in Trondheim, Norway, and a Physicist at the Center for Radiation Research at the National Bureau of Standards. …

10: 18.1 Notation

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$x$-Differences

►Forward differences: … ►Backward differences: … ►Central differences in imaginary direction: … ►In Koekoek et al. (2010) ${\delta }_x$ denotes the operator $\mathrm{i}{\delta }_x$.