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21: 1.10 Functions of a Complex Variable
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►Let and be real or complex numbers that are not integers.
The function
is many-valued with branch points at .
…One such branch is obtained by assigning and their principal values (§4.2(iv)).
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►If the path also circles
times in the clockwise or negative sense before returning to , then the value of becomes .
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§1.10(xi) Generating Functions
…22: 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. | |
… | |
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.)
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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 .
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24: 17.1 Special Notation
§17.1 Special Notation
►(For other notation see Notation for the Special Functions.) … ►The main functions treated in this chapter are the basic hypergeometric (or -hypergeometric) function , the bilateral basic hypergeometric (or bilateral -hypergeometric) function , and the -analogs of the Appell functions , , , and . ►Another function notation used is the “idem” function: …25: 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
…26: 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
…27: 23.2 Definitions and Periodic Properties
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§23.2(i) Lattices
… ► … ►§23.2(ii) Weierstrass Elliptic Functions
… ► ►§23.2(iii) Periodicity
…28: 16.2 Definition and Analytic Properties
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§16.2(i) Generalized Hypergeometric Series
… ► … ►Unless indicated otherwise it is assumed that in the DLMF generalized hypergeometric functions assume their principal values. … ►Polynomials
… ►§16.2(v) Behavior with Respect to Parameters
…29: 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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