# Tagged Questions

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### lower bound of modified Besselfunction

i'm looking for an lower bound for the modified Bessel function of the first kind $I_\nu(x)$ of a +ive real argument. There should be one of the form $$ce^{x^\alpha} \le I_\nu(x)$$.
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### integral with bessel function represented as a series [duplicate]

Possible Duplicate: prove equality with integral and series This integral was my homework question with $p=2$ and $n=1$. I am wondering if one can get the general formula for p, or at least ...
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### Expansions of Hermite functions

I am wondering if someone knows good references. I am looking for expansions of Hermite functions, which gives connections between rates of decay and smoothness of coefficients. Thank you for your ...
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Let $n$ be half an odd integer, say $n=k+1/2, k \in \mathbb{N}$. Let $q\geq 1$. I would like to calculate (or approximate) the following integral: $$\int_0^{\infty}\left(\sqrt{\frac{\pi}{2}}\cdot ... 1answer 1k views ### Projection of Gaussian in Spherical Coordinates Consider a point with spherical coordinates \vec{r}_0=(r_0, \theta_0, 0). The spherical gaussian distribution centered at \vec{r}_0 is f(\vec{r})=Ne^{|\vec{r}-\vec{r}_0|^2/A}, where N is the ... 2answers 1k views ### Easy approximation of the incomplete beta function \text{B}_x(a,b) I need to calculate \text{B}_x(a,b) on the cheap, without too many coefficients and loops. For the complete \text{B}(a,b), I can use \Gamma(a)\Gamma(b)/\Gamma(a+b), and Stirling's approximation ... 1answer 355 views ### Approximating Lambert W for input below 0 As a small part of a much bigger project, I need to be able to approximate the numerical output of the Lambert W function. I have found decent approximations (good up to at least 4 decimal places), ... 3answers 1k views ### efficient and accurate approximation of error function I am looking for the numerical approximation of error function, which must be efficient and accurate. Thanks in advance$$\mathrm{erf}(z)=\frac2{\sqrt\pi}\int_0^z e^{-t^2} \,\mathrm dt
I am looking for a good approximation for the $W_0$ branch of the Lambert $W$ function. I am looking for values $0 < x < e$ only, so I expect something simpler than the general Taylor expansion. ...
### Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?
The $\Gamma (x)$ function has just one minimum for $x>0$ . This result uses some properties of the gamma function: $\Gamma ^{\prime \prime }(x)>0$ and $\Gamma (x)>0$ for all $x>0$ \$\Gamma (1)=\Gamma ...