All Questions
5 questions
1
vote
2
answers
174
views
Confused about the output of `CosIntegral`
I am interested in the properties of the cosine integral function, in this case the anti-derivative of Cos[Pi*x]/x, which Mathematica evaluates to ...
- 2,335
2
votes
3
answers
164
views
Evaluate using Mathematica or otherwise $\int_{0}^{\pi/2}\sin^n x \ T_n(\sin x)\ dx$
Denote $T_n(x)$ as Chebyshev polynomial of the first kind (see here). Then I need to evaluate for $n$ a odd natural number $$\int_{0}^{\pi/2}\sin^n x \ T_n(\sin x)\ dx $$
I am requesting a code with ...
- 301
6
votes
4
answers
993
views
Evaluate the defining Integral of the Bessel functions of the first kind
I am trying to evaluate the integrals
$$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}(x\sin t - nt)} \mathrm{d}t $$
and
$$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t $$
...
- 343
0
votes
1
answer
187
views
Indefinite Integral for rational trigonometric functions without hypergeometric functions
How to find indefinite integrals for the rational trigonometric functions of the form
$\qquad\Lambda^{pq}_m = \int \frac{\cos^p x\sin^q x}{(a+b\sin x +c\cos x)^m} dx$
where $(p,q,m)>0$ using ...
- 115
19
votes
1
answer
851
views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi }...
- 23.1k