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21: 25.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►The main function treated in this chapter is the Riemann zeta function
.
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►The main related functions are the Hurwitz zeta function
, the dilogarithm , the polylogarithm (also known as Jonquière’s function
), Lerch’s transcendent , and the Dirichlet -functions
.
nonnegative integers. | |
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primes | on function symbols: derivatives with respect to argument. |
22: 11.10 Anger–Weber Functions
§11.10 Anger–Weber Functions
… ►§11.10(v) Interrelations
… ►§11.10(vi) Relations to Other Functions
… ► … ►§11.10(viii) Expansions in Series of Products of Bessel Functions
…23: 12.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
►The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: , , , and .
…An older notation, due to Whittaker (1902), for is .
The notations are related by .
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24: 12.14 The Function
§12.14 The Function
… ►For the modulus functions and see §12.14(x). … ►Bessel Functions
… ►Confluent Hypergeometric Functions
… ►Positive ,
…25: 30.1 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 eigenvalues and the spheroidal wave functions
, , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
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Other Notations
…26: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
►§4.37(i) General Definitions
… ►Each of the six functions is a multivalued function of . … ►Other Inverse Functions
… ►§4.37(vi) Interrelations
…27: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
►§4.23(i) General Definitions
… ►Other Inverse Functions
… ►§4.23(viii) Gudermannian Function
… ►The inverse Gudermannian function is given by …28: 23.2 Definitions and Periodic Properties
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§23.2(i) Lattices
… ► … ►§23.2(ii) Weierstrass Elliptic Functions
… ► … ►The function is quasi-periodic: for , …29: 14.1 Special Notation
§14.1 Special Notation
►(For other notation see Notation for the Special Functions.) … ►Multivalued functions take their principal values (§4.2(i)) unless indicated otherwise. ►The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions). …30: 35.1 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 multivariate gamma and beta functions, respectively and , and the special functions of matrix argument: Bessel (of the first kind) and (of the second kind) ; confluent hypergeometric (of the first kind) or and (of the second kind) ; Gaussian hypergeometric or ; generalized hypergeometric or .
►An alternative notation for the multivariate gamma function is (Herz (1955, p. 480)).
Related notations for the Bessel functions are (Faraut and Korányi (1994, pp. 320–329)), (Terras (1988, pp. 49–64)), and (Faraut and Korányi (1994, pp. 357–358)).
complex variables. | |
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