Heun%20operator
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1: 31.1 Special Notation
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►The main functions treated in this chapter are , , , and the polynomial .
…Sometimes the parameters are suppressed.
, | real variables. |
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2: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
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31.5.2
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►These solutions are the Heun polynomials.
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3: 31.2 Differential Equations
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§31.2(i) Heun’s Equation
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31.2.1
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§31.2(ii) Normal Form of Heun’s Equation
… ►§31.2(v) Heun’s Equation Automorphisms
… ►Composite Transformations
…4: 31.17 Physical Applications
§31.17 Physical Applications
►§31.17(i) Addition of Three Quantum Spins
… ►§31.17(ii) Other Applications
… ►For applications of Heun’s equation and functions in astrophysics see Debosscher (1998) where different spectral problems for Heun’s equation are also considered. …5: 31.13 Asymptotic Approximations
§31.13 Asymptotic Approximations
… ►For asymptotic approximations of the solutions of Heun’s equation (31.2.1) when two singularities are close together, see Lay and Slavyanov (1999). ►For asymptotic approximations of the solutions of confluent forms of Heun’s equation in the neighborhood of irregular singularities, see Komarov et al. (1976), Ronveaux (1995, Parts B,C,D,E), Bogush and Otchik (1997), Slavyanov and Veshev (1997), and Lay et al. (1998).6: 31.10 Integral Equations and Representations
§31.10 Integral Equations and Representations
… ►where is Heun’s operator in the variable : … ►Kernel Functions
… ►Kernel Functions
… ►7: 31.4 Solutions Analytic at Two Singularities: Heun Functions
§31.4 Solutions Analytic at Two Singularities: Heun Functions
… ►To emphasize this property this set of functions is denoted by … ►The eigenvalues satisfy the continued-fraction equation … ►The set depends on the choice of and . ►The solutions (31.4.3) are called the Heun functions. …8: 31.12 Confluent Forms of Heun’s Equation
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Confluent Heun Equation
… ►Doubly-Confluent Heun Equation
… ►Biconfluent Heun Equation
… ►Triconfluent Heun Equation
… ►9: 31.6 Path-Multiplicative Solutions
§31.6 Path-Multiplicative Solutions
►A further extension of the notation (31.4.1) and (31.4.3) is given by ►
31.6.1
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