say, where P(x) = P(x; [alpha]) is the residual function which is the sum of the residues of the generating function, [phi](s) to be defined below, with weights and we are to express the error term [DELTA](x; [delta]) in terms of special functions and where the prime on the summation sign
means that the term corresponding to ([n.sub.1] + [[alpha].sub.1]) ...
where the prime over the summation sign
indicates that the summation is over even values of r when n - 1 is even and over odd values of r when n - 1 is odd.
The summation sign
seems to be missing from equation (2) for simple duration.
Take the summation sign
over the first two growth rates and then over the next two rates on the right-hand side.
Also, if the summation sign
appears without an index, by convention the index is understood to go from 1 to n, and we sum all the values of the variable.
However, where the summation sign
is inserted into Equation 1 to make Equation 4 influences the component measures' construction.
In the second term of (12), relocate the summation sign
inside the integral.
where [A.sub.[lambda]](x) = [A.sup.0.sub.[lambda]] (x) = [summation over ([[lambda].sub.k [less than or equal] x])]' '[[alpha].sub.k], and the prime on the summation sign
means that when [[lambda].sub.k] = x, the correponding term is to be halved.
First, for the two terms preceding the summation signs
, we have that [D.sub.a](x)C(x)[D.sub.b-1](x) [less than or equal to] [D.sub.a-1](x)C(x)[D.sub.b](x) since C(x) has non-negative coefficients, and by our induction hypothesis, [D.sub.a](x)[D.sub.b-1](x) [less than or equal to] [D.sub.a-1](x)[D.sub.b](x).
we cannot interchange the summation signs
because the integral defining the sampling functions [[integral].sup.[infinity].sub.0] y(x, [[lambda].sub.n])y(x,[lambda])dx diverges if [lambda] [not equal to] [[lambda].sub.n] and so a Shannon type sampling theorem is not possible for [PW.sup.e].sub.[infinity]] without the knowledge of the type b.
Mordechai Gutman's surgical procedures report, the surgical summation signed
by five of Dr.
where we sum over both i and j and require two summation signs
. We sum over the rows first to obtain column totals and then add these to get the grand total.