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Math Help - Taylor and Maclaurin series

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    Taylor and Maclaurin series

    Find the Taylor and Maclaurin series of the given function with the given point z_0 as center and determine the radius of convergence.

    e^{\frac{z^2}{2}}\int e^{-t^2} dt

    By the way, integrate from 0 to z and center at z_0 = 0

    I cannot imagine, how can I solve this.
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    Quote Originally Posted by noppawit View Post
    Find the Taylor and Maclaurin series of the given function with the given point z_0 as center and determine the radius of convergence.

    e^{\frac{z^2}{2}}\int e^{-t^2} dt

    By the way, integrate from 0 to z and center at z_0 = 0

    I cannot imagine, how can I solve this.
    centered at 0 ...

    e^u = 1 + u + \frac{u^2}{2!} + \frac{u^3}{3!} + ...

    e^{-t^2} = 1 - t^2 + \frac{t^4}{2!} - \frac{t^6}{3!} + ...

    \int_0^z e^{-t^2} \, dt = \left[t - \frac{t^3}{3} + \frac{t^5}{5 \cdot 2!} - \frac{t^7}{7 \cdot 3!} + ... \right]_0^z = z - \frac{z^3}{3} + \frac{z^5}{5 \cdot 2!} - \frac{z^7}{7 \cdot 3!} + ...
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