Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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282 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
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291 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
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216 views

About calculating Integrals

I am trying to Integrate the following Integral (all of the variables are reals) $$\int Exp(-(\cos^{-1}\left[\frac{\text{n}_0 (\text{v}_0-\text{x}_0)+\text{n}_1 (\text{v}_1-\text{x}_1)+\text{n}_2 (u \...
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406 views

Simple contour integral with a parameter gone wrong

Bug introduced in 7.0 and fixed in 7.0.1 I run into the following problem, I tried to evaluate a very simple integral: ...
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38 views

Setting derivative of function equal to 0 at x=0 using UpValues

I'm trying to set the derivative of a function to zero at a specified point. This will act as an initial condition for an algorithm I'm writing: so I'm specifying the value of the function at x=0, and ...
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64 views

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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102 views

Product of two Meijer's Function

I want to evaluate an integral $I_1$ defined in $Eq.(1)$ as \begin{align} I_1=\int_{0}^{\infty}\frac{x\exp(-\beta x)K_1(\alpha x)}{1+x}dx\tag{1} \end{align} Where $\alpha\geq0$, $\beta\geq0$, and $...
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126 views

How do I calculate this integral along a complex line (not a contour) in mathematica?

Given the function: $$f(z) = \frac{\pi ^2 \cot(\pi \sqrt z) \cot(\pi \sqrt {z-a})}{4\sqrt{z^2 - az}}$$ Where a is a positive constant and: $$z = \frac{i}{b} + t $$ $$t>a$$ Where b is also a ...
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43 views

When evaluating this integral Mathematica returns two different answers

When evaluating this integral in Mathematica 10.3 Student Edition: ...
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147 views

A triple integral involving Abs over an ellipsoidal region

I'm a newbie and I'm trying to calculate a triple integral. But Mathematica doesn't output for half an hour and the CPU occupancy rate of my Wolfram doesn't changed when it's calculating. Here is the ...
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135 views

Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
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90 views

Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
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60 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
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55 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
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159 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
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0answers
64 views

Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image. Basically, I do have two data sets A (x1,y1) and ...
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52 views

Computing integral involving derivatives

I want to evaluate an expression $\int_C g(\nabla f)ds$. This is an integration along a curve $C$ in a plane given as a function of some parameter $s$: ...
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782 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
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137 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
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163 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
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111 views

Can NIntegrate be used with the Levin method in several dimensions?

I've got some data in the form of an interpolating function. It's a function of three variables, $\rho(x,y,z)$. I'd basically like to integrate this with some phase over a cube of known size, like $$ ...
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118 views

Giving hints to Integrate

I working with the integral ...
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384 views

Differential equations with a complex variable

Is Mathematica able to handle ordinary differential equations where the variable itself is complex? I am looking for solutions of ODE systems of the form $$\left\{ \begin{align} i\frac{da_1}{dt} &=...
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81 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
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91 views

Help wanted in evaluating an integral

Trying to evaluate an integral. To be specific, I'm trying to find the expectation value of $x^2$ for the ground state of hydrogen. Here is the code I used: ...
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117 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
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170 views

Calculating derivatives of roots of equation

I am interested in calculating how the roots of an equation change as one of the variables does, when the equation is evaluated numerically rather than symbolically. I have edited this code to be ...
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0answers
162 views

Simple Jacobians, Gradients, etc. with arbitrary length vectors/matrices?

Is there any way (or a package built for it) can do simple operations with vectors and matricies of arbitrary size, but conforming extents? For the simplest example to test, given an arbitrary vector ...
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106 views

Help with Integrals (and conditional expectations) of the Beta distribution: Integrate[e^(az) z^a (1-z)^b, {z, 0, 1}]

I have a Beta distribution, and am interested in calculating expectations and conditional expectations. The domain on the distribution is $z \in [0,1]$ Ignoring constants of proportionality, the ...
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585 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
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0answers
1k views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
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39 views

NIntegrate and Integrate seem to over-estimate an integral involving a sharp Lorentzian (Cauchy) distribution

I am trying to do a numerical integral with NIntegrate, but it seems that I get a bigger number than I should. The integral is fairly simple: ...
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34 views

NSolve on a function with NIntegrate

I have a function defined with an NIntegrate. The function is of x,y,z, integrated across t: ...
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0answers
42 views

Numerical derivative step size

I am trying to perform a numerical derivative of some function using ND. I want to know if there is a way to set the step size of differentiation to the specific ...
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0answers
73 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
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41 views

Replace higher order derivatives given lower order derivative

I have an unknown function f[x1,x2] whose partial with respect to x1 is identically zero. I would like to make sure that ...
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38 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
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0answers
60 views

Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
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23 views

Syntax Error with Expectation over Distribution

I am getting some errors when I try to execute the following code. Here, the expectation is taken over $g$ which has Nakagami Distribution. ...
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0answers
27 views

Jackson integral applied to a recursion

Two days ago I asked a question about the way to compute a Jackson integral $\int_0^t h(x[s]) d_qs$. But now, I must applied it in the follwing recursion : $ \left\{\begin{array}{l} x_0[t,q] = f[t]\\...
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57 views

Integrate an expression and simplify the result

I have to find the indefinite integral of the following: $$\int\sqrt{ax^4 + bx^3 + cx^2 + dx + e} dx$$ where a, b, c, d, e are constant of the order 0.0001 or less but always greater than 0. I ...
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65 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
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77 views

Setting up and solving an equation

I would like to solve the equations: $$ F(\xi;x,t)=\int_0^\xi u_{0}(\xi)\:d\xi+\frac{(x-\xi)^{2}}{2t} $$ to use in evaluating: $$ u(x,t)=\dfrac{\int_{-\infty}^\infty \dfrac{x-\xi}{t} e^{-1/2ReF}d\xi}...
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33 views

How can I get left-sided-sequence with InverseZTransform

InverseZTransform[z^2/((4 - z)*(z - 1/4)), z, n, Assumptions -> {1/4 < Abs[z] < 4}] (* -(1/15) 4^-n (-1 + 16^(1 + n)) *) the result is not true.It only ...
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188 views

Implicit hidden assumptions of Mathematica with Limit

I've stumbled upon the following symbolic limit (a tricky one): Limit[(Sqrt[2] v)/Sqrt[v^2 - c^2 (1 - 1/c Sqrt[c^2 - v^2])], v -> 0] Mathematica gives 0 as ...
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53 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
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0answers
35 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
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0answers
16 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
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79 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
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84 views

Mathematica: Derivative appears to be wrong

I'm first getting f(x) by computing an implicit equation. Then I want to take the derivative. Later on, when I plot both f(x) ...