# 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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### Find analytic solution for integral only defined for even integers

I would like to calculate the integral $$\int_0^{2\pi} dx \sin^6\left(\frac{x}{2}\right) F\left(\frac{4-n}{2}, \frac{4+n}{2}, \frac{1}{2}, \cos^2 \frac{x}{2} \right)^2$$ where $F$ is the ...
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### Why doesn't Integrate evaluate an elliptic integral?

My code is Integrate[ 1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, ∞}, Assumptions -> 0 < d < c < b < a] I know this can be ...
159 views

### Why is my integral not being evaluated?

I am trying to integrate a function Gamma, but the output returns the input. I have the following code: ...
68 views

### Error in Taylor's Series using Mathematica

How many terms should be used in taylor series expansion of the function f(z) = e^z around z = 0 for a specific value of z = 30 + 30 i to get an error of less than 0.05 using Mathematica? ...
385 views

### Calculating curvature of a contour

I have an equation of a scalar field in the form $$f(x, y) = x^2 + y^2 + xy + c$$ I want to find the curvature of the contour of the curve at $f_c = f(0.5, 0.5)$. So I need to calculate the ...
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### Why Integrate does not obtain this conditional result automatically for orthogonality of cosines?

V 12.1 on windows. I remember asking something similar many years ago. I was hoping Mathematica now could have done this automatically: $$\int_{-\pi}^{\pi} \cos (n x) \cos (m x) \, dx$$ For ...
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### Why doesn't Mathematica simplify? [closed]

Consider the following: Simplify[Integrate[x^(a), {x, x1, x2}], x1 > 0 && x2 > 0 && a > 0] Mathematica doesn't simplify this for me. I ...
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### Kramers-Kronig relations

I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica. ...
52 views