scaled spheroidal wave functions
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11: 9.12 Scorer Functions
12: 11.9 Lommel Functions
§11.9 Lommel Functions
… ► ►Reflection Formulas
… ►§11.9(ii) Expansions in Series of Bessel Functions
… ►13: 20.2 Definitions and Periodic Properties
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§20.2(i) Fourier Series
… ►§20.2(ii) Periodicity and Quasi-Periodicity
… ►The theta functions are quasi-periodic on the lattice: … ►§20.2(iii) Translation of the Argument by Half-Periods
… ►§20.2(iv) -Zeros
…14: 16.13 Appell Functions
§16.13 Appell Functions
►The following four functions of two real or complex variables and cannot be expressed as a product of two functions, in general, but they satisfy partial differential equations that resemble the hypergeometric differential equation (15.10.1): ►
16.13.1
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16.13.4
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15: 5.12 Beta Function
16: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
►§14.20(i) Definitions and Wronskians
… ► … ►§14.20(ii) Graphics
… ►§14.20(x) Zeros and Integrals
…17: 10.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
For the other functions when the order is replaced by , it can be any integer.
For the Kelvin functions the order is always assumed to be real.
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
18: 4.2 Definitions
19: 16.2 Definition and Analytic Properties
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