Dedekind%20eta%20function
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1: 23.15 Definitions
§23.15 Definitions
… ►§23.15(ii) Functions , ,
►Elliptic Modular Function
… ►Dedekind’s Eta Function (or Dedekind Modular Function)
… ►2: 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
…3: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
… ► … ►§14.20(ii) Graphics
… ►The variable is defined implicitly by …The interval is mapped one-to-one to the interval , with the points and corresponding to and , respectively. …4: 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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5: 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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6: 5.15 Polygamma Functions
§5.15 Polygamma Functions
►The functions , , are called the polygamma functions. In particular, is the trigamma function; , , are the tetra-, penta-, and hexagamma functions respectively. Most properties of these functions follow straightforwardly by differentiation of properties of the psi function. … ►For see §24.2(i). …7: 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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5.2.2
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