Formula:4467

Digital Library of Mathematical Functions ID 10.57.E1

${\displaystyle{\displaystyle\mathsf{j}_{n}'\left((n+\tfrac{1}{2})z\right)=\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}J_{n+\frac{1}{2}}'\left((n+\tfrac{1}{2})z\right)-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}J_{n+\frac{1}{2}}\left((n+\tfrac{1}{2})z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}$: spherical Bessel function of the first kind
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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