of periodic functions
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21—30 of 70 matching pages
21: 24.17 Mathematical Applications
22: Bibliography I
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The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
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Further investigations into the periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
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23: 1.8 Fourier Series
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βΊFormally, if is a real- or complex-valued -periodic function,
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βΊLet be an absolutely integrable function of period
, and continuous except at a finite number of points in any bounded interval.
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βΊIf a function
is periodic, with period
, then the series obtained by differentiating the Fourier series for term by term converges at every point to .
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24: 25.11 Hurwitz Zeta Function
25: 4.16 Elementary Properties
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βΊ
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26: 28.2 Definitions and Basic Properties
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βΊ
§28.2(vi) Eigenfunctions
…27: 24.16 Generalizations
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βΊIn no particular order, other generalizations include: Bernoulli numbers and polynomials with arbitrary complex index (Butzer et al. (1992)); Euler numbers and polynomials with arbitrary complex index (Butzer et al. (1994)); q-analogs (Carlitz (1954a), Andrews and Foata (1980)); conjugate Bernoulli and Euler polynomials (Hauss (1997, 1998)); Bernoulli–Hurwitz numbers (Katz (1975)); poly-Bernoulli numbers (Kaneko (1997)); Universal Bernoulli numbers (Clarke (1989)); -adic integer order Bernoulli numbers (Adelberg (1996)); -adic -Bernoulli numbers (Kim and Kim (1999)); periodic Bernoulli numbers (Berndt (1975b)); cotangent numbers (Girstmair (1990b)); Bernoulli–Carlitz numbers (Goss (1978)); Bernoulli–Padé numbers (Dilcher (2002)); Bernoulli numbers belonging to periodic functions (Urbanowicz (1988)); cyclotomic Bernoulli numbers (Girstmair (1990a)); modified Bernoulli numbers (Zagier (1998)); higher-order Bernoulli and Euler polynomials with multiple parameters (Erdélyi et al. (1953a, §§1.13.1, 1.14.1)).