Formula:3999

Digital Library of Mathematical Functions ID 10.21.E18

${\displaystyle{\displaystyle\frac{\mathrm{d}c^{\prime}}{\mathrm{d}\nu}=\frac{2c^{\prime}}{{c^{\prime}}^{2}-\nu^{2}}\*\int_{0}^{\infty}({c^{\prime}}^{2}\cosh\left(2t\right)-\nu^{2})\*K_{0}\left(2c^{\prime}\sinh t\right)e^{-2\nu t}\mathrm{d}t,}}$

Symbols List

• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle c}}$: zero of cylinder function
 

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