Formula:3066

Digital Library of Mathematical Functions ID 7.6.E9

${\displaystyle{\displaystyle\operatorname{erf}\left(az\right)=\frac{2z}{\sqrt{\pi}}e^{(\frac{1}{2}-a^{2})z^{2}}\sum_{n=0}^{\infty}T_{2n+1}\left(a\right){\mathsf{i}^{(1)}_{n}}\left(\tfrac{1}{2}z^{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-1\leq a\leq 1}}$

Symbols List

• ${\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}$: Chebyshev polynomial of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}$: error function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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