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21: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
… ►The Riemann zeta function is a special case: … ►§25.11(ii) Graphics
… ►§25.11(vi) Derivatives
…22: 25.1 Special Notation
…
►(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
.
…
►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. | |
… | |
primes | on function symbols: derivatives with respect to argument. |
23: 12.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
…
►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 .
…
24: 17.1 Special Notation
§17.1 Special Notation
►(For other notation see Notation for the Special Functions.) ►nonnegative integers. | |
… |
25: 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
…26: 23.2 Definitions and Periodic Properties
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§23.2(i) Lattices
… ► … ►§23.2(ii) Weierstrass Elliptic Functions
… ► ►§23.2(iii) Periodicity
…27: 12.14 The Function
§12.14 The Function
… ►§12.14(vii) Relations to Other Functions
►Bessel Functions
… ►Confluent Hypergeometric Functions
… ►§12.14(x) Modulus and Phase Functions
…28: 30.1 Special Notation
…
►(For other notation see Notation for the Special Functions.)
…
►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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