In Section 2.1, the numerical method of random Gauss-Hermite for the evaluation of random improper integrals
is introduced and it is applied to an example strategically placed that will be used later in Section 3, where problem (1.1)-(1.2) is firstly analytically solved using the random Fourier transform.
And Section 3 is devoted to the definition of the Aumann fuzzy improper integral
. In Section 4, fuzzy Laplace transform is introduced, its basic properties are studied, and a particular case of Laplace convolution is investigated.
Secondly, we need to obtain the approximation of the improper integral
We think that this phenomenon was caused by the improper integral
constant, which makes us underestimate the IPS.
Moreover, suitable analytical acceleration techniques to fast evaluate the obtained improper integrals
of oscillating and slowly decaying functions has been developed.
provided this limit exists, and one says that the improper integral
converges in this case.
To see that the second integral in (3) converges, we use the comparison test for improper integrals
. Since f(t) is of exponential order 1/[k.sup.2], we have for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and hence:
Then the function [u.sub.1] given by the improper integral
Then the improper integral
of first kind of the form [[infinity].sup.[infinity].sub.a] f(t)g(t)[DELTA]t is convergent.
Let us assume that the improper integrals
converge correctly and that we can keep a finite number of terms in the approximation of the integral:
creating an improper integral
. These properties of p.d.f.'s would
Maher); (60) Didactical Knowledge Development of Pre-Service Secondary Mathematics Teachers (Pedro Gomez and Luis Rico); (61) Legitimization of the Graphic Register in Problem Solving at the Undergraduate Level: The Case of the Improper Integral