# piecewise continuous functions

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## 1—10 of 15 matching pages

##### 1: 6.16 Mathematical Applications

##### 2: 1.4 Calculus of One Variable

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►For an example, see Figure 1.4.1
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►If ${\varphi}^{\prime}(x)$ is continuous or piecewise continuous, then
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##### 3: 3.7 Ordinary Differential Equations

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►Let $(a,b)$ be a finite or infinite interval and $q(x)$ be a real-valued continuous (or piecewise continuous) function on the closure of $(a,b)$.
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##### 4: 1.5 Calculus of Two or More Variables

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►A function
$f(x,y)$ is

*piecewise continuous*on ${I}_{1}\times {I}_{2}$, where ${I}_{1}$ and ${I}_{2}$ are intervals, if it is piecewise continuous in $x$ for each $y\in {I}_{2}$ and piecewise continuous in $y$ for each $x\in {I}_{1}$. …##### 5: 1.8 Fourier Series

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►If ${a}_{n}$ and ${b}_{n}$ are the Fourier coefficients of a piecewise continuous function
$f(x)$ on $[0,2\pi ]$, then
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##### 6: 2.3 Integrals of a Real Variable

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►In addition to (2.3.7) assume that $f(t)$ and $q(t)$ are piecewise continuous (§1.4(ii)) on $(0,\mathrm{\infty})$, and
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##### 7: 1.14 Integral Transforms

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►If $f(t)$ is continuous and ${f}^{\prime}(t)$ is piecewise continuous on $[0,\mathrm{\infty})$, then
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►If $f(t)$ is piecewise continuous, then
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►Also assume that ${f}^{(n)}(t)$ is piecewise continuous on $[0,\mathrm{\infty})$.
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►If $f(t)$ and $g(t)$ are piecewise continuous, then
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►If $f(t)$ is piecewise continuous on $[0,\mathrm{\infty})$ and the integral (1.14.47) converges, then
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##### 8: 18.2 General Orthogonal Polynomials

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►Here $w(x)$ is continuous or piecewise continuous or integrable such that
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►This happens, for example, with the continuous Hahn polynomials and Meixner–Pollaczek polynomials (§18.20(i)).
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►The measure is not necessarily absolutely continuous (i.
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►Nevai (1979, p.39) defined the class $\mathcal{S}$ of orthogonality measures with support inside $[-1,1]$ such that the absolutely continuous part $w(x)dx$ has $w$ in the Szegő class $\mathcal{G}$.
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###### Monotonic Weight Functions

…##### 9: 10.43 Integrals

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(b)
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###### §10.43(i) Indefinite Integrals

… ►###### §10.43(iii) Fractional Integrals

… ► … ►The*Kontorovich–Lebedev transform*of a function $g(x)$ is defined as … ►$g(x)$ is piecewise continuous and of bounded variation on every compact interval in $(0,\mathrm{\infty})$, and each of the following integrals

##### 10: 18.18 Sums

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