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1: 6.2 Definitions and Interrelations
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§6.2(i) Exponential and Logarithmic Integrals
… ►As in the case of the logarithm (§4.2(i)) there is a cut along the interval and the principal value is two-valued on . … ►The logarithmic integral is defined by … ► is an odd entire function. … ►§6.2(iii) Auxiliary Functions
…2: 5.2 Definitions
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§5.2(i) Gamma and Psi Functions
►Euler’s Integral
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5.2.1
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►It is a meromorphic function with no zeros, and with simple poles of residue at .
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5.2.3
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3: 9.12 Scorer Functions
4: 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
…5: 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
…6: 5.12 Beta Function
7: 14.19 Toroidal (or Ring) Functions
§14.19 Toroidal (or Ring) Functions
►§14.19(i) Introduction
… ►§14.19(ii) Hypergeometric Representations
… ►§14.19(iv) Sums
… ►§14.19(v) Whipple’s Formula for Toroidal Functions
…8: 23.15 Definitions
§23.15 Definitions
►§23.15(i) General Modular Functions
… ►Elliptic Modular Function
… ►Dedekind’s Eta Function (or Dedekind Modular Function)
… ►9: 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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