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21: Bibliography

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Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.

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Notes:

Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous, Translation revised by the authors and James Montaldi

External Links:

ISBN 0-8176-3185-2, MathReview, ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX

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22: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►and functions $f(x),g(x)\in C^2(a,b)$, assumed real for the moment. … ►For $𝒟(T)$ we can take $C^2(X)$, with appropriate boundary conditions, and with compact support if $X$ is bounded, which space is dense in $L^2\left(X\right)$, and for $X$ unbounded require that possible non-$L^2$ eigenfunctions of (1.18.28), with real eigenvalues, are non-zero but bounded on open intervals, including $\pm \mathrm{\infty }$. … ►For $f(x)$ piecewise continuously differentiable on $[0,\mathrm{\infty })$ … ►, $f\in C^2(X)$) of $Lf=zf$ which is moreover in $L^2\left(X\right)$. …

23: 3.7 Ordinary Differential Equations

… ►If $q(x)$ is $C^{\mathrm{\infty }}$ on the closure of $(a,b)$, then the discretized form (3.7.13) of the differential equation can be used. …

24: 3.8 Nonlinear Equations

… ►This is an iterative method for real twice-continuously differentiable, or complex analytic, functions: …

25: 18.38 Mathematical Applications

… ►In consequence, expansions of functions that are infinitely differentiable on $[-1,1]$ in series of Chebyshev polynomials usually converge extremely rapidly. …

26: 30.13 Wave Equation in Prolate Spheroidal Coordinates

… ►If $b_1=b_2=0$, then the function (30.13.8) is a twice-continuously differentiable solution of (30.13.7) in the entire $(x,y,z)$-space. …

27: 22.16 Related Functions

… ► $\mathrm{am}(x,k)$ is an infinitely differentiable function of $x$. …

28: 2.10 Sums and Sequences

… ►Secondly, when $f(z)-g(z)$ is $m$ times continuously differentiable on $|z|=r$ the result (2.10.29) can be strengthened. …

29: 3.3 Interpolation

… ►If $f$ and the $z_k$ ($=x_k$) are real, and $f$ is $n$ times continuously differentiable on a closed interval containing the $x_k$, then …

30: 10.43 Integrals

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On the interval , $x^{-1}g(x)$ is continuously differentiable and each of $xg(x)$ and $xd(x^{-1}g(x))/dx$ is absolutely integrable.

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