- #1

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## Main Question or Discussion Point

Does anyone know how to go about solving

[itex]\int e^{(x^{2})} dx[/itex]

[itex]\int e^{(x^{2})} dx[/itex]

- Thread starter metrictensor
- Start date

- #1

- 117

- 1

Does anyone know how to go about solving

[itex]\int e^{(x^{2})} dx[/itex]

[itex]\int e^{(x^{2})} dx[/itex]

- #2

- 998

- 0

[tex]\int e^{(x^2)} \ dx = -\frac{i\sqrt{\pi}}{2}\mbox{erf}(ix)+C.[/tex]

Essentially what this means is that you either have to compute definite integrals with this integrand numerically, or look up values on tables for the error function.

- #3

- 117

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This is helpful. I have the bounds. Thaks. It is weird that there is no analytical solution to something that looks so simple. I did write a taylor series and integrated that to get an infinite sum that is equal to the integral. It is:Data said:

[tex]\int e^{(x^2)} \ dx = -\frac{i\sqrt{\pi}}{2}\mbox{erf}(ix)+C.[/tex]

Essentially what this means is that you either have to compute definite integrals with this integrand numerically, or look up values on tables for the error function.

[itex]

\sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)n!}}

[/itex]

- #4

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that's like the *classic* example of something that has no elementary solution...

- #5

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The "erf" function is tabulated for real arguments only...

Daniel.

Daniel.

- #6

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https://www.amazon.com/exec/obidos/...002-0334771-5287233?v=glance&s=books&n=507846

:tongue:

- #7

- 12,988

- 543

Give me a link to the page in A & Stegun where the erf function of complex arg is tabulated.

Daniel.

Daniel.

- #8

- 12,988

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Direct link.

http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150&Page=325&Submit=Go

Daniel.

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