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1: 31.14 General Fuchsian Equation

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$\alpha \beta ={\displaystyle \sum _{j=1}^N}{a}_j{q}_j.$

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2: 16.21 Differential Equation

… ►With the classification of §16.8(i), when the only singularities of (16.21.1) are a regular singularity at $z=0$ and an irregular singularity at $z=\mathrm{\infty }$. …

3: 16.8 Differential Equations

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§16.8(i) Classification of Singularities

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4: 17.4 Basic Hypergeometric Functions

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§17.4(iv) Classification

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5: 31.2 Differential Equations

… ►All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, $ℂ\cup \{\mathrm{\infty }\}$, can be transformed into (31.2.1). …

6: 31.12 Confluent Forms of Heun’s Equation

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7: 37.2 General Orthogonal Polynomials of Two Variables

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§37.2(viii) The Krall–Sheffer classification

… ►The other four cases in the classification are for weight functions which take both positive and negative values. … ►Xu (2005) gave a similar classification of admissible second order partial difference operators, i. …One of the OPs resulting from this classification are the Hahn polynomials of two variables, see §37.10(iv). …

8: 2.7 Differential Equations

… ►All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients. … ►To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing $z$ in (2.7.1) with $1/z$; see Olver (1997b, pp. 153–154). … ►This phenomenon is an example of resurgence, a classification due to Écalle (1981a, b). …

9: 37.13 General Orthogonal Polynomials of $d$ Variables

… ►Analogous to the Krall–Sheffer classification in the two-variable case (see §37.2(viii)), one can ask for admissible $d$-variable second order PDOs $L$, i. … ►For the $d$-variable case there is no classification result in the literature similar to the one by Krall and Sheffer for $d=2$. …

10: 2.8 Differential Equations with a Parameter

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§2.8(i) Classification of Cases

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