wave functions
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1: 30.1 Special Notation
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►The main functions treated in this chapter are the eigenvalues and the spheroidal wave functions
, , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
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Other Notations
►Flammer (1957) and Abramowitz and Stegun (1964) use for , for , and …2: 30.11 Radial Spheroidal Wave Functions
§30.11 Radial Spheroidal Wave Functions
►§30.11(i) Definitions
… ►Connection Formulas
… ►§30.11(ii) Graphics
… ► …3: 30.10 Series and Integrals
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4: 30 Spheroidal Wave Functions
Chapter 30 Spheroidal Wave Functions
…5: 30.5 Functions of the Second Kind
6: 30.6 Functions of Complex Argument
7: 30.4 Functions of the First Kind
§30.4 Functions of the First Kind
►§30.4(i) Definitions
… ►If , reduces to the Ferrers function : … ►§30.4(ii) Elementary Properties
… ►§30.4(iv) Orthogonality
…8: 30.12 Generalized and Coulomb Spheroidal Functions
§30.12 Generalized and Coulomb Spheroidal Functions
►Generalized spheroidal wave functions and Coulomb spheroidal functions are solutions of the differential equation …9: 30.15 Signal Analysis
§30.15 Signal Analysis
►§30.15(i) Scaled Spheroidal Wave Functions
… ►§30.15(ii) Integral Equation
… ► … ►10: 30.17 Tables
§30.17 Tables
… ►Flammer (1957) includes 18 tables of eigenvalues, expansion coefficients, spheroidal wave functions, and other related quantities. Precision varies between 4S and 10S.
Zhang and Jin (1996) includes 24 tables of eigenvalues, spheroidal wave functions and their derivatives. Precision varies between 6S and 8S.