In this case, a constant C is included; however, in the following cases it will be omitted, on the assumption that readers are aware that indefinite integrals should always include a constant.
Similarly to the case of square roots, a number of methods for evaluating indefinite integrals have been developed for more difficult situations.
[30.] Rosenheinrich, W., Tables of Some Indefinite Integrals
of Bessel Functions, 2003, http://www.fh-jena.de/~rsh/Forschung/Stoer /besint.pdf.
It is assumed that the functions [y.sub.rd] and [y.sub.rq] to be the indefinite integral of the functions [g.sup.-1.sub.d] and [g.sup.-1.sub.q] in the rotor reference frame, respectively.
By using the effective air gap function of the eccentric SPSM and determining its indefinite integral, precise analytical equations for inductances have been obtained.
A first remark is that fx [subset] A[P.sub.r] (R, C) must have the indefinite integral
in the same space.
Proposition 19) the indefinite integral of Pettis integrable function is weakly absolutely continuous and it is pseudo differentiable with respect to the right endpoint of the integration interval and its pseudo derivative equals the integrand at that point.
The claim now follows immediately, since the indefinite integral of weakly contentious function is weakly absolutely continuous and it is weakly differentiable with respect to the right endpoint of the integration interval and its weak derivative equals the integrand at that point.
Using an integral representation formula and an indefinite integral of the Bessel function, we determined the structure of single and multiple electromagnetic imaging functions.
[27.] Rosenheinrich, W., "Tables of some indefinite integrals of bessel functions," Available at http://www.fh-jena.de/rsh/Forschung/ Stoer/besint.pdf.
We will explore the use of three CAS's in the evaluation of indefinite integrals
: Maple 11, Mathematica 6.0.2 and the Texas Instruments (TI) 89 Titanium graphics calculator.
and we truncate the infinite summations at j = [+ or -]N in such a way that N and the mesh size h satisfies h = 1/N log(2[pi]dN/[alpha])or 1/N log([pi]dN/[alpha]), for definite or indefinite integrals