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sphericalBessJ

sphericalBessJ (n, x [, accuracy])​

The sphericalBessJ function returns the spherical Bessel function of the first kind and order n.

jn(x)=π2xJn+1/2(x).\displaystyle j_{n}(x)=\sqrt{\frac{\pi}{2 x}} J_{n+1 / 2}(x) .

For example:

j0(x)=sin⁡(x)xj1(x)=sin⁡(x)x2−cos⁡(x)xj2(x)=(3x3−1x)sin⁡(x)−3x2cos⁡(x).\begin{array}{l} \displaystyle j_{0}(x)=\frac{\sin (x)}{x} \\ \\ \displaystyle j_{1}(x)=\frac{\sin (x)}{x^{2}}-\frac{\cos (x)}{x} \\ \\ \displaystyle j_{2}(x)=\left(\frac{3}{x^{3}}-\frac{1}{x}\right) \sin (x)-\frac{3}{x^{2}} \cos (x) . \end{array}

Details​

See the bessI function for details on accuracy and speed of execution.

See Also​

sphericalBessJD, sphericalBessY

References​

Abramowitz, M., and I.A. Stegun, "Handbook of Mathematical Functions", 446 pp., Dover, New York, 1972.