# Questions tagged [calculus-and-analysis]

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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### Workarounds for unevaluated results of ContourIntegrate of non-analytic functions

There is a new useful command ContourIntegrate since 13.3. I find that the command is well-done, but even the Sun has spots. ...
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### Strange result simplifying higher order BesselJ

Consider the following integral: $$\int_0^1 Z_n^m(r)\ J_m(\rho r) r dr$$. The solution of this should contain a single Bessel function: $$(-1)^{(m-n)/2}\ J_{n+1} (\rho)/\rho$$ (see https://www.osti....
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### How to make Assumptions in IntegrateChangeVariables?

There is a new useful command IntegrateChangeVariables since 13.1. The command has the Assumptions option which is very poorly ...
1 vote
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### How do I integrate with respect to one variable when an integrand has many variables?

I am trying to integrate the following integrand: (μ*a*curr/4 π)*((x - a*Cos[ϕ] + y - a*Sin[ϕ])/ ((x - a*Cos[ϕ])^2 + (y - a*Sin[ϕ])^2)^(3/2)) with the following ...
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### Digits of Pi in colored spiral

In How to make the digits of π go around in a spiral like this? it is described how to plot pi in a spiralform (in my case as binary number): ...
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### Help implementing Lagrange inversion

I'm attempting to find the coefficients of generating functions using Lagrange inversion. I am finding the series coefficients with: ...
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### Implementing positivity constraints over a six-dimensional hypercube

This question involves the same subject matter as my previous one (How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?), but with another (...
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### Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
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### Numerical Integration without giving all values [closed]

Is there a way to solve expressions numerically, while keeping other variables. For example, I want to Integrate the expression below for $\theta p,\theta q$ while keeping other things as it is. The ...
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### How to linearize these terms in many different variables? [duplicate]

How to linearize these terms in q[t] and p[t,y] ...
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### Seeking Wolfram Mathematica Techniques for Detailed Step-by-Step Solution of Integral Equation Transformation [closed]

Hello Mathematica Community, I am working on a mathematical problem where I need to transform an integral equation into a simpler form using Euler's Formula and the Error Function. My current ...
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### How to linearize this equation in two different variables?

How to linearize this equation in two different variables p[t] and q[t,y]: ...
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### Principal value of a double integral numerically

I have several integrals of the form : where and . where a,b,wc and T are constants and PV denotes the Cauchy principal value I tried to integrate one of this form using NIntegrate however when ...
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### Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
1 vote
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### First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
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### Symbolic partial differentiation of a Lagrangian function including a summation

I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
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### Limit giving indeterminate result

I have a function $r_h(v)$ given by, $$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$ where $m_0$ and $g$ are just numbers. I want to take the limits of ...
1 vote
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### How to prevent evaluation without simplification?

I am trying to compute a sequence of terms, which have a form similar to $g(z)$ at different points $z$. For $z$ close to 0, I have observed that the terms are evaluated as 0/0 (indeterminate form) ...