Neville%20theta%20functions
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21: 12.14 The Function
§12.14 The Function
… ►Bessel Functions
… ►Confluent Hypergeometric Functions
… ►where is defined in (12.14.5), and (0), , (0), and are real. or is the modulus and or is the corresponding phase. …22: 22.2 Definitions
§22.2 Definitions
… ►where and the theta functions are defined in §20.2(i). … ► … ►The six functions containing the letter in their two-letter name are odd in ; the other six are even in . ►In terms of Neville’s theta functions (§20.1) …23: 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. |
24: 12.1 Special Notation
…
►(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 .
…
25: 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: …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
… ► ►§23.2(iii) Periodicity
…29: 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
…30: 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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