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piecewise continuous

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1: 6.16 Mathematical Applications
It occurs with Fourier-series expansions of all piecewise continuous functions. … …
2: 1.4 Calculus of One Variable
For an example, see Figure 1.4.1
See accompanying text
Figure 1.4.1: Piecewise continuous function on [ a , b ) . Magnify
If ϕ ( x ) is continuous or piecewise continuous, then … If f ( x ) is continuous or piecewise continuous on [ a , b ] , then …
3: 1.8 Fourier Series
If f ( x ) is of period 2 π , and f ( m ) ( x ) is piecewise continuous, then … For f ( x ) piecewise continuous on [ a , b ] and real λ , … If a n and b n are the Fourier coefficients of a piecewise continuous function f ( x ) on [ 0 , 2 π ] , then …
4: 1.14 Integral Transforms
If f ( t ) is continuous and f ( t ) is piecewise continuous on [ 0 , ) , then … If f ( t ) is piecewise continuous, then … Also assume that f ( n ) ( t ) is piecewise continuous on [ 0 , ) . … If f ( t ) and g ( t ) are piecewise continuous, then … If f ( t ) is piecewise continuous on [ 0 , ) and the integral (1.14.47) converges, then …
5: 18.2 General Orthogonal Polynomials
Here w ( x ) is continuous or piecewise continuous or integrable, and such that 0 < a b x 2 n w ( x ) d x < for all n . …
6: 1.5 Calculus of Two or More Variables
A function f ( x , y ) is piecewise continuous on I 1 × I 2 , where I 1 and I 2 are intervals, if it is piecewise continuous in x for each y I 2 and piecewise continuous in y for each x I 1 . … Sufficient conditions for the limit to exist are that f ( x , y ) is continuous, or piecewise continuous, on R . … Moreover, if a , b , c , d are finite or infinite constants and f ( x , y ) is piecewise continuous on the set ( a , b ) × ( c , d ) , then …
7: 3.7 Ordinary Differential Equations
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 ) . …
8: 18.18 Sums
Alternatively, assume f ( x ) is real and continuous and f ( x ) is piecewise continuous on ( - 1 , 1 ) . … Assume f ( x ) is real and continuous and f ( x ) is piecewise continuous on ( 0 , ) . … Assume f ( x ) is real and continuous and f ( x ) is piecewise continuous on ( - , ) . …
9: 1.17 Integral and Series Representations of the Dirac Delta
More generally, assume ϕ ( x ) is piecewise continuous1.4(ii)) when x [ - c , c ] for any finite positive real value of c , and for each a , - e - n ( x - a ) 2 ϕ ( x ) d x converges absolutely for all sufficiently large values of n . …
10: 2.3 Integrals of a Real Variable
In addition to (2.3.7) assume that f ( t ) and q ( t ) are piecewise continuous1.4(ii)) on ( 0 , ) , and …