repeated

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21—30 of 30 matching pages

21: Bibliography

… ►

D. E. Amos (1989) Repeated integrals and derivatives of

K

Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt
Referenced by:: §10.43(iii).
Encodings:: BibTeX

…

22: 3.6 Linear Difference Equations

… ►The process is then repeated with a higher value of

N

, and the normalized solutions compared. …

23: 3.7 Ordinary Differential Equations

… ►By repeated differentiation of (3.7.1) all derivatives of

w(z)

can be expressed in terms of

w(z)

and

w^{\prime}(z)

as follows. …

24: 15.5 Derivatives and Contiguous Functions

… ►By repeated applications of (15.5.11)–(15.5.18) any function

F\left(a+k,b+\ell;c+m;z\right)

, in which

k,\ell,m

are integers, can be expressed as a linear combination of

F\left(a,b;c;z\right)

and any one of its contiguous functions, with coefficients that are rational functions of

a, b, c

, and

z

. …

25: 1.9 Calculus of a Complex Variable

… ►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 …

26: 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 …

27: 19.36 Methods of Computation

… ►Numerical differences between the variables of a symmetric integral can be reduced in magnitude by successive factors of 4 by repeated applications of the duplication theorem, as shown by (19.26.18). …

28: 2.11 Remainder Terms; Stokes Phenomenon

… ►Often the process of re-expansion can be repeated any number of times. …

29: 10.21 Zeros

… ►This inaccuracy was repeated in Abramowitz and Stegun (1964, Figures 9.5 and 9.6). …

30: 10.22 Integrals

… ►When

\alpha=m=1,2,3,\ldots

the left-hand side of (10.22.36) is the

m

th repeated integral of

J_{\nu}\left(x\right)

(§§1.4(v) and 1.15(vi)). …