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21: 1.8 Fourier Series
1.8.1 f ( x ) = 1 2 a 0 + n = 1 ( a n cos ( n x ) + b n sin ( n x ) ) ,
Let f ( x ) be an absolutely integrable function of period 2 π , and continuous except at a finite number of points in any bounded interval. … For other tests for convergence see Titchmarsh (1962, pp. 405–410). … If a n and b n are the Fourier coefficients of a piecewise continuous function f ( x ) on [ 0 , 2 π ] , then … If a function f ( x ) C 2 [ 0 , 2 π ] is periodic, with period 2 π , then the series obtained by differentiating the Fourier series for f ( x ) term by term converges at every point to f ( x ) . …
22: 27.18 Methods of Computation: Primes
An analytic approach using a contour integral of the Riemann zeta function25.2(i)) is discussed in Borwein et al. (2000). … These algorithms are used for testing primality of Mersenne numbers, 2 n - 1 , and Fermat numbers, 2 2 n + 1 . … The APR (Adleman–Pomerance–Rumely) algorithm for primality testing is based on Jacobi sums. … The AKS (Agrawal–Kayal–Saxena) algorithm is the first deterministic, polynomial-time, primality test. …
23: 3.5 Quadrature
which depends on function values computed previously. … For effective testing of Gaussian quadrature rules see Gautschi (1983). …
Gauss Formula for a Logarithmic Weight Function
Example
24: 1.9 Calculus of a Complex Variable
Differentiation
Analyticity
Harmonic Functions
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