Publication: Functional estimates for derivatives of the modified Bessel function and related exponential functions
Functional estimates for derivatives of the modified Bessel function and related exponential functions
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Falletta, S., & Sauter, S. A. (2014). Functional estimates for derivatives of the modified Bessel function and related exponential functions. Journal of Mathematical Analysis and Applications, 417(2), 559–579. https://doi.org/10.1016/j.jmaa.2014.03.057
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Let K0K0 denote the modified Bessel function of second kind and zeroth order. In this paper we will study the function View the MathML sourceω˜n(x):=(−x)nK0(n)(x)n! for positive argument. The function View the MathML sourceω˜n plays an important role for the formulation of the wave equation in two spatial dimensions as a retarded potential integral equation. We will prove that the growth of the derivatives View the MathML sourceω˜n(m) with respect to n can be bounded by O((n+1)m/2)O((n+1)m/2) while for small and large arguments x
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- Falletta, Silvia
- Sauter, Stefan A
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Falletta, S., & Sauter, S. A. (2014). Functional estimates for derivatives of the modified Bessel function and related exponential functions. Journal of Mathematical Analysis and Applications, 417(2), 559–579. https://doi.org/10.1016/j.jmaa.2014.03.057
