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1: 5.2 Definitions
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§5.2(i) Gamma and Psi Functions
►Euler’s Integral
… ►It is a meromorphic function with no zeros, and with simple poles of residue at . is entire, with simple zeros at . ►
5.2.2
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2: 20.2 Definitions and Periodic Properties
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§20.2(i) Fourier Series
… ►§20.2(ii) Periodicity and Quasi-Periodicity
►For fixed , each is an entire function of with period ; is odd in and the others are even. … ►The theta functions are quasi-periodic on the lattice: … ►§20.2(iv) -Zeros
…3: 15.2 Definitions and Analytical Properties
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§15.2(i) Gauss Series
►The hypergeometric function is defined by the Gauss series … … ►§15.2(ii) Analytic Properties
►The principal branch of is an entire function of , , and . …4: 9.12 Scorer Functions
§9.12 Scorer Functions
… ►where … ► and are entire functions of . … ► … ►Functions and Derivatives
…5: 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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6: 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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