q-differential equations
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1: 17.6 Function
2: 17.2 Calculus
3: 17.13 Integrals
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17.13.3
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4: 28.12 Definitions and Basic Properties
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§28.12(i) Eigenvalues
… βΊFor given (or ) and , equation (28.2.16) determines an infinite discrete set of values of , denoted by , . When Equation (28.2.16) has simple roots, given by … … βΊIf is a normal value of the corresponding equation (28.2.16), then these functions are uniquely determined as analytic functions of and by the normalization …5: 28.10 Integral Equations
6: 28.2 Definitions and Basic Properties
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βΊThe standard form of Mathieu’s equation with parameters is
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28.2.1
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βΊFor given and , equation (28.2.16) determines an infinite discrete set of values of , the eigenvalues or characteristic
values, of Mathieu’s equation.
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Change of Sign of
… βΊFor simple roots of the corresponding equations (28.2.21) and (28.2.22), the functions are made unique by the normalizations …7: 18.27 -Hahn Class
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βΊTogether they form the
-Askey scheme.
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βΊIn the -Hahn class OP’s the role of the operator in the Jacobi, Laguerre, and Hermite cases is played by the -derivative , as defined in (17.2.41).
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βΊFor other formulas, including -difference equations, recurrence relations, duality formulas, special cases, and limit relations, see Koekoek et al. (2010, Chapter 14).
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