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Differentiating Bessel functions

Alexmahone

Active member
Jan 26, 2012
268
Differentiate $x^{1/2}\left[c_1J_{1/4}(x^2/2)+c_2J_{-1/4}(x^2/2)\right]$.
 

chisigma

Well-known member
Feb 13, 2012
1,704
Differentiate $x^{1/2}\left[c_1J_{1/4}(x^2/2)+c_2J_{-1/4}(x^2/2)\right]$.
A general formula is...

$\displaystyle J_{\nu}^{'}(x)= \frac{1}{2}\ \{J_{\nu-1}(x)-J_{\nu+1}(x)\}$ (1)

Kind regards

$\chi$ $\sigma$