auxiliary%20functions%20for%20Fresnel%20integrals
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1: 7.2 Definitions
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►
§7.2(i) Error Functions
… ►§7.2(ii) Dawson’s Integral
… ►§7.2(iii) Fresnel Integrals
… ► , , and are entire functions of , as are and in the next subsection. … ►§7.2(iv) Auxiliary Functions
…2: 23.15 Definitions
§23.15 Definitions
►§23.15(i) General Modular Functions
… ►Elliptic Modular Function
… ►Dedekind’s Eta Function (or Dedekind Modular Function)
… ►3: 5.2 Definitions
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►
§5.2(i) Gamma and Psi Functions
►Euler’s Integral
►
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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►
5.2.2
.
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4: 9.12 Scorer Functions
5: 14.19 Toroidal (or Ring) Functions
§14.19 Toroidal (or Ring) Functions
►§14.19(i) Introduction
… ►§14.19(iii) Integral Representations
… ►§14.19(iv) Sums
… ►§14.19(v) Whipple’s Formula for Toroidal Functions
…6: 11.9 Lommel Functions
§11.9 Lommel Functions
… ► ►Reflection Formulas
… ►§11.9(ii) Expansions in Series of Bessel Functions
… ►7: 5.12 Beta Function
8: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
… ► … ►§14.20(ii) Graphics
… ►§14.20(iv) Integral Representation
… ►§14.20(x) Zeros and Integrals
…9: 9.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
►
►
►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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