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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Pull Constants outside of integrals

I would like Mathematica to pull constants outside of an integral: e.g., $\int_0^t f[t] g[s] dt \to g[s] \int_0^t f[t] dt$ This has previously been discussed at replacement rule to pull independent ...
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1answer
101 views

Simple Question: Derivative of a path

I have a path V[t_]:={3t^2,2,6t}, and I define F[t_]:=V[t]/Norm[V[t]]. I simply want the derivative of ...
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1answer
60 views

Integral over geometric region [duplicate]

I'd like to calculate this integral $$ \int_E y\ dydz $$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...
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0answers
79 views

Complex Convolution

I am attempting to integrate a convolution variable using the following code. However, the program is taking too long to complete the integration. Does anybody have any coding tips that may make ...
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1answer
57 views

Integrate and NIntegrate yield different results for double integral

Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with {10, 3} and {8, 1.5} as ...
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0answers
29 views

How to calculate this derivative? [duplicate]

Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$ \frac{\partial F}{\partial x_m} = \sum_n 2 x_n ...
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0answers
49 views

Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
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41 views

A regularized hypergeometric function related question

I'm interested in finding a way (if possible) of expressing this specific value of the regularized hypergeometric function in terms of known constants. How might I use Mathematica to check this ...
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0answers
19 views

Does this Sum converge? [migrated]

I need to solve Does this converge or diverge?
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0answers
58 views

Evaluating an indefinite integral at the boundaries

I have the following expression i need to integrate over $\alpha$ from 0 to 1 and $x$ from $x1$ to $\infty$ ...
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1answer
44 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
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0answers
45 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
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1answer
30 views

Defining arbitrary order derivatives function [duplicate]

I have a function $\phi(t)$ and I want to define a function $\phi D(t,r):=\phi^{(r)}(t)$, in other words evaluate the $r$'th derivative of $\phi$ at $t$. The naive code that I have is: ...
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0answers
72 views

A power series expansion

Consider the function, $f(z) = z tanh(\pi z) log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ and ...
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67 views

About how Mathematica understands the branchcuts of the complex logarithm [Part 3]

One understands that for the function $\log(z^2+a^2)$ Mathematica implicitly puts the branch cuts to be starting at $\pm ia$ and going up/down respectively on the imaginary axis. The phase of this ...
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46 views

problem solving a simple integral equation

I'm looking for a function q(x) so that integral( q(t) , t , x, x+2*pi/3) == a*sin(x)+b Could anyone help me on this one? Thx in advance
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58 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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52 views

Derivative of generating function (Example from documentation)

In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative: ...
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1answer
48 views

NIntegrate and NumericQ [closed]

I need to do numerical integration --> differentiation --> numerical integration. I tried to apply the technique described in the accepted answer to a similar question: ...
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0answers
30 views

Is it possible to obtain vector differentiation results in terms of vectors rather than components? [duplicate]

When doing certain operations on vectors in Mathematica it is quite desirable to convert the results back into coordinate-free notation. Unfortunately, after going through the Documentation Center and ...
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71 views

Numerical Differentiation of an interpolated list.

I have a synthetic spectrum with a wavelength range of .3 to .7 microns. I have interpolated this spectrum for re-sampling purposes. However, I am also attempting to calculate the first and second ...
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46 views

Errors while computing some terms of the Euler–Maclaurin formula

Here is an issue I came across while I was applying one of the well-known versions of Euler–Maclaurin formula. I try to realize why Mathematica goes wrong with this code below ...
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55 views

An error message with NIntegrate and inability to plot the integrand

I took a function of x which depended on parameters on m,n,a,y and then first summed up the n from -Infinity to Infinity and then I set the other parameters to some random values and then I asked it ...
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3answers
247 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
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1answer
85 views

Mathematica does not solve this integral [closed]

I want to compute the integral of a polynomial in t, which I know an analitical solution exist. But Mathematica give me as result the input, not the result of the integral: I already know this ...
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1answer
41 views

Excluding an interval of parameters from Integrate [duplicate]

I'd like to compute an integral that depends on a parameter, but I'd like to exclude an interval from the computation. For concreteness, say I want to compute ...
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0answers
62 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...
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0answers
75 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
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0answers
76 views

Cannot calculate an integral

I am new to Mathematica. So I just run a basic procedure but Mathematica didn't calculate this integral. Maybe it is too complicated to be done. ...
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0answers
53 views

PDE syntax question

I am trying to solve a PDE of a reaction diffusion equation, and while I'm getting a decent looking solution, I am also getting inconsistent BC / initial conditions warnings and wanted to check if my ...
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0answers
65 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
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0answers
54 views

limit calculation step by step [duplicate]

I calculate such limit with Mathematica: ...
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0answers
50 views

Reducing a long complex expression to a simplier one by using assumptions

so I have an ugly looking equation that I wish to solve under some specific circumstances. Using DSolve I write; ...
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140 views
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117 views

Approximating a stochastic integral with a Wiener process

I would like some assistance to solve the following: $\sum\limits_{i=0}^{n-1} e^{-k(n\Delta t -i\Delta t)}\Delta z_i$ where $z$ is a Wiener process, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
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1answer
125 views

Better way to evaluate integral containing Boolean function

I am trying to compute the integral ...
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0answers
95 views

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...
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0answers
90 views

Interpretation of output derivative expression [duplicate]

I am trying to write Mathematica file to find Div, Grad, Laplacian, etc. in coordinates ...
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0answers
33 views

Plot derivative of integral with changing limits [duplicate]

My code is: Plot[D[Integrate[E^(t*(-x^2)),{x,t+2,t^2}],t],{t,-2,3}]. The errors/warnings are: ...
-1
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3answers
121 views

Computing integral over explicit region [closed]

I need to integrate $f(x,y)=y^2-2x^2y+6x^3-3xy+2y-6x$ over $\{y\geq 2x^2-2, y\leq 3x\}$ Im using Boole in the following way; ...
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3answers
673 views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
-1
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1answer
130 views

Solving an equation for asymptotic dependence of the solution on a coefficient

I have an equation I want to solve, so I entered the following into Mathematica. (x^(17/6))/(a^(17/6)) - (x^2)/a -1 == 0 where I assume $a>>1$ and $x$ is ...
-1
votes
1answer
104 views

Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
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1answer
153 views

Limit of a subsequence

I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same. I was able to generate the sum for ...
-4
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1answer
333 views

Symbolic Definite Integration

How do I perform Integrate[Sin[x]^2/(z^2 + R^2 - 2 zRCos[x])^(3/2), {x, 0, Pi}] where z and ...
-5
votes
1answer
118 views

Help in coding of differential equations [closed]

I need some help with Mathematica. How can I do the following? Starting with f = y[0]^2 (y[0] is basically y with 0 subscript) ...
-6
votes
1answer
119 views

Alternative closed forms for digamma expressions

What commands should I use such that Mathematica / W|A express $$\psi(1+i)+\psi(1-i)$$ exclusively in terms of trigonometric functions?