mean value property for harmonic functions
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31: 30.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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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
…32: 14.1 Special Notation
§14.1 Special Notation
►(For other notation see Notation for the Special Functions.) … ►Multivalued functions take their principal values (§4.2(i)) unless indicated otherwise. ►The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions). …33: 22.15 Inverse Functions
§22.15 Inverse Functions
►§22.15(i) Definitions
… ►Each of these inverse functions is multivalued. The principal values satisfy …and unless stated otherwise it is assumed that the inverse functions assume their principal values. …34: 28.12 Definitions and Basic Properties
§28.12 Definitions and Basic Properties
… ►§28.12(ii) Eigenfunctions
… ►If 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 …They have the following pseudoperiodic and orthogonality properties: … ►These functions are real-valued for real , real , and , whereas is complex. …35: 30.11 Radial Spheroidal Wave Functions
§30.11 Radial Spheroidal Wave Functions
►§30.11(i) Definitions
… ►Connection Formulas
… ►§30.11(ii) Graphics
… ►§30.11(iv) Wronskian
…36: 1.16 Distributions
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