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1: 1.10 Functions of a Complex Variable
Then z = z 0 is an isolated singularity of f ( z ) . …Lastly, if a n 0 for infinitely many negative n , then z 0 is an isolated essential singularity. … In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception. …
2: 32.2 Differential Equations
be a nonlinear second-order differential equation in which F is a rational function of w and d w / d z , and is locally analytic in z , that is, analytic except for isolated singularities in . …An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however. …
3: 14.32 Methods of Computation
Essentially the same comments that are made in §15.19 concerning the computation of hypergeometric functions apply to the functions described in the present chapter. …
4: 34.12 Physical Applications
The angular momentum coupling coefficients ( 3 j , 6 j , and 9 j symbols) are essential in the fields of nuclear, atomic, and molecular physics. …
5: Notices
The DLMF wishes to provide users of special functions with essential reference information related to the use and application of special functions in research, development, and education. …
6: Guide to Searching the DLMF
DLMF search recognizes just the essential font differences, that is, the font style differences deemed important for the DLMF contents: …
7: Preface
 Stegun, editors); and to disseminate essentially the same information from a public website operated by NIST. …
8: Mathematical Introduction
The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). …
9: 18.37 Classical OP’s in Two or More Variables
In one variable they are essentially ultraspherical, Jacobi, continuous q -ultraspherical, or Askey–Wilson polynomials. …
10: DLMF Project News
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