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minor typographic fixes
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edit approved Nov 10, 2017 at 2:06
J.J. Green
edit approved Nov 10, 2017 at 2:06
J.J. Green
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I am looking at the following function on the domain $x\geq 0$:

$F(x)=(x+a)e^{x^2}(1-erf(x))-\frac{b}{\sqrt\pi}$,$$F(x)=(x+a)e^{x^2}(1-\mathrm{erf}(x))-\frac{b}{\sqrt\pi},$$

where $a>0$, $0<b<1$ are parameters. From plotting this function for different values of $a$ and $b$ it seems that there is at most one root on $x\in[0,\infty)$. But how to prove it?

I am looking at the following function on the domain $x\geq 0$:

$F(x)=(x+a)e^{x^2}(1-erf(x))-\frac{b}{\sqrt\pi}$,

where $a>0$, $0<b<1$ are parameters. From plotting this function for different values of $a$ and $b$ it seems that there is at most one root on $x\in[0,\infty)$. But how to prove it?

I am looking at the following function on the domain $x\geq 0$:

$$F(x)=(x+a)e^{x^2}(1-\mathrm{erf}(x))-\frac{b}{\sqrt\pi},$$

where $a>0$, $0<b<1$ are parameters. From plotting this function for different values of $a$ and $b$ it seems that there is at most one root on $x\in[0,\infty)$. But how to prove it?

Post Reopened by Fedor Petrov, Stefan Kohl♦, Francois Ziegler, Iosif Pinelis, Noah Schweber
edited tags; edited title
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Iosif Pinelis
Iosif Pinelis
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A calculus problem involving the Error Function

Post Closed as "Not suitable for this site" by Alexey Ustinov, Stefan Waldmann, Loïc Teyssier, Alex Degtyarev, R.P.
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Jackie Lu
Jackie Lu
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A calculus problem involving the Error Function

I am looking at the following function on the domain $x\geq 0$:

$F(x)=(x+a)e^{x^2}(1-erf(x))-\frac{b}{\sqrt\pi}$,

where $a>0$, $0<b<1$ are parameters. From plotting this function for different values of $a$ and $b$ it seems that there is at most one root on $x\in[0,\infty)$. But how to prove it?