# Tagged Questions

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### Real roots plot of the modified bessel function

Could anyone point me a program so i can calculate the roots of $$K_{ia}(2 \pi)=0$$ here $K_{ia}(x)$ is the modified Bessel function of second kind with (pure complex)index 'k' :D My conjecture ...
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### Kummer U function: U(a,a+1/2,z)

Is there any way to simplify $U(a,a+1/2,z)$ or relate it to any other common special functions such as the incomplete beta function or the incomplete gamma function? Here, $U(a,b,z)$ is Kummer's U ...
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### Find bound on order of Bessel function

I need to evaluate and store the first significant ($n$) orders for a given abscissa for the Bessel functions of the first kind. That is, $J_v(x), \ v \in [0, n]$. Here significant means that I want ...
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### Calculation of integral with Bessel function

I have a trouble with to calculating (or bounding from above) the following integral: $$\int_{-\infty}^{\infty}\left(\frac{J_2(x)}{x^2}\right)^p\, dx, \quad p\geq 1,$$ where $J_2(x)$ is a Bessel ...
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### How to calculate Bessel Function of the first kind fast?

I have wrote a C++ code to calculate the first kind of Bessel Functon by its infinite series definition. I took the sum of the first 20 series as the value of Bessel Function, which is same as MATLBA ...
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### Numerical approximation for log of incomplete beta function

Is there any known numerical approach to directly compute the log of the incomplete beta function? I would like to be able to compute $$\log\left( \int_0^u x^{a-1} (1-x)^{b-1} dx \right)$$ ...
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### Computing the inverse Jacobi function $\mathrm{arccd}$ with elliptic integrals

According to page 42 of 1, $\operatorname{arccd}(x, k)=F\left(\arcsin\left(\sqrt{\frac{1 - x^2}{1 - k^2x^2}}\right), k\right)$, where $F(\phi, k)=\int_0^\phi \frac{dt}{\sqrt{1 - k^2\sin^2t^2}}$, and ...
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### How to compute complete elliptic integral of the first kind in explicit form using elementary functions?

How to compute complete elliptic integral of the first kind in explicit form using elementary functions? If it is not possible to compute complete elliptic integral of the first kind in explicit way, ...
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### Numerical methods for integrals involving product of Bessel functions of the first kind (1st order)

I am looking for the best (in terms of low computation times) numerical methods for calculating the following integrals: $$\int_0^{\infty}\,f(k)\,J_1(ak)\,J_1(bk)\,dk$$ with for instance ...
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### Numerical values of the Jacobi elliptic function sn: Wolfram Alpha vs. Maple vs. C++?

I have a problem to check the validity of an algorithm I've implemented in C++ to compute the Jacobi elliptic function $\mathrm{sn}(u, k)$ (inspired and improved from Numerical Recipes 3rd edition). I ...