Neville%20theta%20functions
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1: 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
…2: 21.2 Definitions
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§21.2(i) Riemann Theta Functions
… ► is also referred to as a theta function with components, a -dimensional theta function or as a genus theta function. … ►Many applications involve quotients of Riemann theta functions: the exponential factor then disappears. … ►§21.2(ii) Riemann Theta Functions with Characteristics
… ►§21.2(iii) Relation to Classical Theta Functions
…3: 23.15 Definitions
§23.15 Definitions
►§23.15(i) General Modular Functions
… ►Elliptic Modular Function
… ►Dedekind’s Eta Function (or Dedekind Modular Function)
… ►4: 14.19 Toroidal (or Ring) Functions
§14.19 Toroidal (or Ring) Functions
►§14.19(i) Introduction
… ►This form of the differential equation arises when Laplace’s equation is transformed into toroidal coordinates , which are related to Cartesian coordinates by … ►§14.19(iv) Sums
… ►§14.19(v) Whipple’s Formula for Toroidal Functions
…5: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
… ► … ►When , … ►From (14.20.9) or (14.20.10) it is evident that is positive for real . … ►uniformly for , where and are the modified Bessel functions (§10.25(ii)) and is an arbitrary constant such that . …6: 5.12 Beta Function
7: 9.1 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 Airy functions
and , and the Scorer functions
and (also known as inhomogeneous Airy functions).
►Other notations that have been used are as follows: and for and (Jeffreys (1928), later changed to and ); , (Fock (1945)); (Szegő (1967, §1.81)); , (Tumarkin (1959)).
nonnegative integer, except in §9.9(iii). | |
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8: 31.1 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 , , , and the polynomial .
…Sometimes the parameters are suppressed.
, | real variables. |
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