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Results tagged with integration
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user 49208
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
5
votes
2
answers
607
views
Integrals involving trigonometric functions and polynomials
Can one describe all the real polynomials $P(x)$ such that the following integrals converge:
$$
\int_0^{\infty} \sin(P(x))dx, \int_0^{\infty} \cos(P(x))dx ?
$$
Among special cases are such celebriti …
- 1,560
5
votes
Evaluating elliptic integrals
It seems to be known as symmetric elliptic integrals of Carlson. Look in the NIST book, 19.15 and further. There are a lot of formulas in it. It seems you seek for exactly the formula 19.22.8 on page …
- 1,560
4
votes
0
answers
204
views
Integral inequality of Polya
In the book Math Problems AMM (1957), Problem 230, there is the next inequality of D. Polya:
let $a,b>0$, $0\leq x \leq a $,
$f(x)$ --- being not a linear function, and $f(0)=0$, $f(a)=b$, $f(x)\geq …
- 1,560
2
votes
Accepted
Laplace transform of : $t^{\gamma-1} F(\alpha,\beta,\delta,t)$, where $F$ is the Gauss' hype...
There is an explicit formula in the book:
A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev. INTEGRALS AND SERIES, Volume 4.
Direct Laplace Transforms. GORDON AND BREACH, 1992.
It is on the page 533 an …
- 1,560
2
votes
2
answers
240
views
Evaluate an integral or Fourier coefficients
Consider an integral
$$
\int_0^\pi \frac{\cos(kx)}{\cosh(ax)}\ dx
$$
there $k\in
\mathbb{Z}, a\in \mathbb{R}.$
Of course that is Fourier coefficient for the function $f(x)=\frac{1}{\cosh(ax)}.$
Ques …
- 1,560
2
votes
What function is "$U_{\nu}(\cdot, \cdot)$"?
This is the Lommel function of two variables, cf. p.748 of the book you mentioned for its definition.
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