# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

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### How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations contain integration, and the integration also contains U and Tf. The main ...
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### Getting rid of sub-exponential terms in an asymptotic expansion for a modified Bessel function

I am trying to get Mathematica to produce suitable asymptotic expansions for some modified Bessel functions at large argument (more specifically, the expansion in the DLMF's eq. (10.40.1)), and I'm ...
32 views

### Replacing expressions with variables [closed]

I have a large matrix where the entries are rational in Jacobi elliptic functions e.g. I'd like to replace the elliptic functions by variables, e.g. ...
159 views

### How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
241 views

### Compile a MeijerG function [duplicate]

I am not very experienced with Compile, I tried to use it for a Meijer-G function ...
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### Simplification of Gamma functions

I am having some trouble simplifying some Gamma functions. I have a large expression in which some combinations of Gamma functions appear, that can be simplified, but applying ...
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### Symbolically Expanding One-Variable $q$-hypergeometric Series

In general, how do I get Mathematica to symbolically expand various infinite series to an arbitrary degree of accuracy? I deal with $q$-hypergeometric series quite frequently, and specifically want ...
185 views

### My code uses ClebschGordan but Mathematica is using ThreeJSymbol

I'm using a function that calculate CG coefficients with the function ClebschGordan but instead, I've got the following error because Mathematica is using ...
73 views

### Solving and Plotting Infinite sums over solutions to transcendental equation involving Bessel functions

I am trying to use Mathematica to plot the following equation $E(q,\Delta)$ vs $qa$, for set values of $D \Delta/a^2$ and $\bar\rho a/D$. I have looked at other stackexchange posts which deal with ...
211 views

### Mathematica implementation of Zeilberger's algorithm (previously done in Maple)

I have this Mathematica code: ...
141 views

### FindSequenceFunction for sum of hypergeometric terms?

The built-in function FindSequenceFunction is quite good at recognizing hypergeometric terms, i.e. terms $c_k$ for which $c_{k+1}/c_k$ is a rational function of $k$....
112 views

### Series expansion of $(x;x)_\infty$ at $x=1^-$?

The so called Euler function is implemented in Mathematica as QPochhammer[x, x] I have been trying to obtain its leading behavior for $x\to 1$ from below. ...
110 views

### Plotting the Schwarz D minimal surface

With the aid of the following paper I'm trying to plot the Schwarz D minimal surface: paper. So far I have followed all the instructions to the best of my abilities and have come up with the following ...
220 views

### Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
232 views

### $\tt SphericalHarmonicY$ does not seem to be an eigenfunction of the spherical harmonic equation

I applied the spherical harmonic equation on the SphericalHarmonicY functions like this: ...
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### Numerical integral of finite valued function over finite integral fails with NIntegrate::inumri

I have the following (simplified) integral: ...
1k views

### Irregular Confluent Hypergeometric Functions (Spherical Coulomb Wavefunctions)

I want to program in the regular and irregular spherical Coulomb wavefunctions $F_\ell(\gamma,kr)$ and $G_\ell(\gamma,kr)$, respectively, which are defined in terms of the regular and irregular ...
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### How is it possible that PolyLog[2,1.1] returns an imaginary number?

Given that: PolyLog is defined as li[n_, z_] := Sum[z^k/k^n, {k, 1, ∞}], ...
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### Spherical Hankel and Bessel in Explicit form

This is probably an easy question, when I type the spherical Hankel (first kind) and the Bessel function into Wolfram Alpha, it gives back an explicit form, the one you would get if you were to do it ...
277 views

### NIntegrate and Integrate of a Spherical Bessel function

I am trying to integrate a spherical Bessel function. I have used both the Integrate and NIntegrate functions in Mathematica but ...
125 views

### Why NIntegrate is badly-behaved on $J_{\frac{9}{2}}(x)$ by default?

A friend of mine showed me this example: Plot[BesselJ[9/2, x], {x, 0, 1}, PlotLabel -> Style["The integrand seems to be simple", 14]] ...
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### How to invert an Elliptic function where the elliptic nome is a function of an independent variable?

I have a Jacobian elliptic function as a function of two independent variables $x$ and $y$. The elliptic parameter $m=m(y)$, $0 \leq m \leq 1$, is also a function of the variable $y$, and thus the ...
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### Weird behavior of HypergeometricPFQ

Consider the following function: fun = HypergeometricPFQ[{1, x1-y1, 1-x1-y1-2u}, {x2-y1, 3-x2-y1-2u}, 1]; Let us try and evaluate this function on the following ...
140 views

### NIntegrate fails in a very strange way

I found a strange behavior in Mathematica when trying to evaluate the integral $$f(n) = \int_{1}^2 \frac{\Gamma(n)\Gamma(x)}{\Gamma(x+n)}{\rm d}x$$ I evaluate this using ...
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### Clothoid (using Fresnel Integrals) [closed]

A clothoid is represented by The Problem Given the following functions, use Mathematica's Fresnel Integrals to plot the curve. My Attempt ...
1k views

### How to change machineprecision digits

I am trying to compute t0: ...
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### Calculating sum of BesselJ[n, x]

My friend has a sum in his research paper that looks like this $$\sum_{n=-\infty}^{\infty}\frac{J_n^2(x)}{n-\kappa}.$$ He was able to calculate this sum analytically, by substituting the denominator ...
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### How to do this integral of Hypergeometric functions in Mathematica?

I've tried to integrate by part, but it seems that Mathematica is still not able to integrate. ...
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### How to get ContourPlot3D to run involving elliptic functions?

I need to plot zeroes of a function of three variables that involves elliptic functions. For example, I have ...
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### Determine parameter from which on there is no more root for a given function

Let $\gamma>0$ be a real number and $\Phi(r)=\frac{1}{r}-\frac{\pi}{4}\left(H_0(r/2)-Y_0(r/2)\right)$ defined on $[0,\infty)$, where $H_0$ is the Struve function of order zero and $Y_0$ is the ...
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### Round off in Mathematica Built-in functions [duplicate]

Is there a way to force Mathematica to use its Built-in functions instead basic functions? For instance, the Hypergeometric1F1[a,b,x] function has a exponential form when its firsts parameters are ...
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### How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...
81 views

### Interval arithmetic for DawsonF (or other special functions)

I am currently trying to estimate a complicated expression involving DawsonF using interval arithmetic. The interval arithmetic is partially supported by ...
304 views

### Can your Mathematica do the following integral?

Backslide introduced in v10 and fixed in v10.4.1. I was trying to do the following integral in Mathematica: Integrate[(z-2) PolyLog[2,z]Log[1-z]/z^3,z] What I ...
103 views

### Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
251 views

### Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J....
44 views

### QPochhammer function simplification?

Consider the function which in Mathematica is denoted as QPochhammer[a,q,n], and its infinite product cousine: which in Mathematica reads ...
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### Wrong numerical results from LegendreP

{Cos[Pi/180] // N, LegendreP[46, 0.9998476951563913`], LegendreP[46, Cos[Pi/180]] // N} give ...
331 views

### Implementation of a complex recurrence relation for polynomials

I would like to implement the recurrence relation for the polynomials $U_n(x)$ appearing in the large order asymptotics of the Bessel functions. The recurrence in question is: U_{n+1}(x)=\frac{1}{...
259 views

### Integrating a BesselJ integrand to obtain the same result as Maple 16

I would like to check the following integration: Integrate[y Integrate[1/x BesselJ[1, x Exp[I π/4]] BesselJ[1, x Exp[-I π/4]], {x, 0, y}], {y, 0, r}] ...
7k views

### About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...