repeated integrals of

(0.002 seconds)

21—23 of 23 matching pages

21: 2.11 Remainder Terms; Stokes Phenomenon

… ►As an example consider … ►From §8.19(i) the generalized exponential integral is given by …However, on combining (2.11.6) with the connection formula (8.19.18), with

m=1

, we derive … ►Often the process of re-expansion can be repeated any number of times. …For integrals, see Berry and Howls (1991), Howls (1992), and Paris and Kaminski (2001, Chapter 6). …

22: 2.4 Contour Integrals

… ►If, in addition, the corresponding integrals with

Q

and

F

replaced by their derivatives

Q^{(j)}

and

F^{(j)}

j=1,2,\dots,m

, converge uniformly, then by repeated integrations by parts …

23: 1.9 Calculus of a Complex Variable

… ►

Cauchy’s Integral Formula

… ►

Poisson Integral

… ►Suppose

\{z_{m,n}\}

converges to

z

and the repeated limits …Then both repeated limits equal

z

. … ►If a double series is absolutely convergent, then it is also convergent and its sum is given by either of the repeated sums …