A Unified Calculus Using the Generalized Bernoulli Polynomials
Copyright policy )A Unified Calculus Using the Generalized Bernoulli Polynomials
The \(\alpha\)-Bernoulli polynomials \(B_{n,\alpha}(x)\) are defined by the generating function \[ {e^{(x- 1/2)z}\over g_\alpha({iz\over 2})}= \sum^\infty_{n= 0} {B_{n,\alpha}(x)\over n!} z^n, \] where \(g_\alpha(z):= 2^\alpha \Gamma(\alpha+ 1)(J_\alpha(z)/z^\alpha)\), the series converges for \(|z| {1\over 2}\).
- Polytechnique Montréal Canada
Mathematics(all), Numerical Analysis, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), \(\alpha\)-Bernoulli polynomials, Applied Mathematics, Remainders in approximation formulas, \(\alpha\)-derivative, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), unified calculus, Approximations and expansions, Analysis, entire functions of exponential type
Mathematics(all), Numerical Analysis, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), \(\alpha\)-Bernoulli polynomials, Applied Mathematics, Remainders in approximation formulas, \(\alpha\)-derivative, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), unified calculus, Approximations and expansions, Analysis, entire functions of exponential type
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