discontinuity
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1: 1.4 Calculus of One Variable
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►A simple discontinuity of at occurs when and exist, but .
If is continuous on an interval save for a finite number of simple discontinuities, then is piecewise (or sectionally) continuous on .
For an example, see Figure 1.4.1
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2: 10.25 Definitions
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►In particular, the principal branch of is defined in a similar way: it corresponds to the principal value of , is analytic in , and two-valued and discontinuous on the cut .
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►The principal branch corresponds to the principal value of the square root in (10.25.3), is analytic in , and two-valued and discontinuous on the cut .
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3: Bibliography W
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Smoothing of Stokes’s discontinuity for the generalized Bessel function. II.
Proc. Roy. Soc. London Ser. A 455, pp. 3065–3084.
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Smoothing of Stokes’s discontinuity for the generalized Bessel function.
Proc. Roy. Soc. London Ser. A 455, pp. 1381–1400.
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4: 10.2 Definitions
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►Except in the case of , the principal branches of and are two-valued and discontinuous on the cut ; compare §4.2(i).
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►The principal branches of and are two-valued and discontinuous on the cut .
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5: 4.15 Graphics
6: 4.24 Inverse Trigonometric Functions: Further Properties
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7: 4.2 Definitions
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►Consequently is two-valued on the cut, and discontinuous across the cut.
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►This is an analytic function of on , and is two-valued and discontinuous on the cut shown in Figure 4.2.1, unless .
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8: 28.12 Definitions and Basic Properties
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►As a function of with fixed (), is discontinuous at .
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9: Bibliography D
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Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities.
Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
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10: 4.37 Inverse Hyperbolic Functions
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