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simple discontinuity

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1: 1.4 Calculus of One Variable
A simple discontinuity of f ( x ) at x = c occurs when f ( c + ) and f ( c - ) exist, but f ( c + ) f ( c - ) . If f ( x ) is continuous on an interval I save for a finite number of simple discontinuities, then f ( x ) is piecewise (or sectionally) continuous on I . For an example, see Figure 1.4.1
2: 28.12 Definitions and Basic Properties
When q = 0 Equation (28.2.16) has simple roots, given by … As in §28.7 values of q for which (28.2.16) has simple roots λ are called normal values with respect to ν . …As a function of ν with fixed q ( 0 ), λ ν ( q ) is discontinuous at ν = ± 1 , ± 2 , . …
3: Bibliography D
  • A. M. Din (1981) A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.
  • B. I. Dunlap and B. R. Judd (1975) Novel identities for simple n - j symbols. J. Mathematical Phys. 16, pp. 318–319.
  • T. M. Dunster (1996b) 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.
  • T. M. Dunster (2001a) Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.
  • T. M. Dunster (2014) Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.