removable%20discontinuity
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11—20 of 143 matching pages
11: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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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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12: 8 Incomplete Gamma and Related
Functions
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13: 28 Mathieu Functions and Hill’s Equation
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14: 18.40 Methods of Computation
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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►Results similar to these appear in Langhoff et al. (1976) in methods developed for physics applications, and which includes treatments of systems with discontinuities in , using what is referred to as the Stieltjes derivative which may be traced back to Stieltjes, as discussed by Deltour (1968, Eq. 12).
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15: 36.2 Catastrophes and Canonical Integrals
16: 1.10 Functions of a Complex Variable
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►This singularity is removable if for all , and in this case the Laurent series becomes the Taylor series.
…Lastly, if for infinitely many negative , then is an isolated essential singularity.
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►An isolated singularity is always removable when exists, for example at .
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►A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed.
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►Branches of can be defined, for example, in the cut plane obtained from by removing the real axis from to and from to ; see Figure 1.10.1.
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17: 25.14 Lerch’s Transcendent
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25.14.1
; .
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18: 26.15 Permutations: Matrix Notation
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►For , denotes after removal of all elements of the form or , .
denotes with the element
removed.
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19: 23.18 Modular Transformations
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23.18.7
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