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11—18 of 18 matching pages

11: 18.18 Sums

… ►Alternatively, assume $f(x)$ is real and continuous and $f^{\prime }(x)$ is piecewise continuous on $(-1,1)$. … ►Assume $f(x)$ is real and continuous and $f^{\prime }(x)$ is piecewise continuous on $(0,\mathrm{\infty })$. … ►Assume $f(x)$ is real and continuous and $f^{\prime }(x)$ is piecewise continuous on $(-\mathrm{\infty },\mathrm{\infty })$. …

12: 1.17 Integral and Series Representations of the Dirac Delta

… ►More generally, assume $\varphi (x)$ is piecewise continuous (§1.4(ii)) when $x\in [-c,c]$ for any finite positive real value of $c$, and for each $a$, ${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\mathrm{e}}^{-n{(x-a)}^2}\varphi (x)dx$ converges absolutely for all sufficiently large values of $n$. …

13: 2.3 Integrals of a Real Variable

… ►In addition to (2.3.7) assume that $f(t)$ and $q(t)$ are piecewise continuous (§1.4(ii)) on $(0,\mathrm{\infty })$, and …

14: 3.11 Approximation Techniques

… ►Splines are defined piecewise and usually by low-degree polynomials. …

15: 10.43 Integrals

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$g(x)$ is piecewise continuous and of bounded variation on every compact interval in $(0,\mathrm{\infty })$, and each of the following integrals

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16: 1.9 Calculus of a Complex Variable

… ►If $x(t)$ and $y(t)$ are continuous and $x^{\prime }(t)$ and $y^{\prime }(t)$ are piecewise continuous, then $z(t)$ defines a contour. …

17: 18.2 General Orthogonal Polynomials

… ►Here $w(x)$ is continuous or piecewise continuous or integrable such that …

18: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For $f(x)$ piecewise continuously differentiable on $[0,\mathrm{\infty })$ …