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1: Viewing DLMF Interactive 3D Graphics
Any installed VRML or X3D browser should be removed before installing a new one. …
2: 5.10 Continued Fractions
3: 1.10 Functions of a Complex Variable
This singularity is removable if a n = 0 for all n < 0 , and in this case the Laurent series becomes the Taylor series. …Lastly, if a n 0 for infinitely many negative n , then z 0 is an isolated essential singularity. … An isolated singularity z 0 is always removable when lim z z 0 f ( z ) exists, for example ( sin z ) / z at z = 0 . … A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed. … Branches of F ( z ) can be defined, for example, in the cut plane D obtained from by removing the real axis from 1 to and from - 1 to - ; see Figure 1.10.1. …
4: 25.14 Lerch’s Transcendent
25.14.1 Φ ( z , s , a ) n = 0 z n ( a + n ) s , | z | < 1 ; s > 1 , | z | = 1 .
5: 26.15 Permutations: Matrix Notation
For ( j , k ) B , B [ j , k ] denotes B after removal of all elements of the form ( j , t ) or ( t , k ) , t = 1 , 2 , , n . B ( j , k ) denotes B with the element ( j , k ) removed. …
6: 23.18 Modular Transformations
23.18.7 s ( d , c ) = r = 1 c - 1 r c ( d r c - d r c - 1 2 ) , c > 0 .
7: 5.6 Inequalities
8: 5.17 Barnes’ G -Function (Double Gamma Function)
9: 1.4 Calculus of One Variable
A removable singularity of f ( x ) at x = c occurs when f ( c + ) = f ( c - ) but f ( c ) is undefined. … …
10: 4.8 Identities
The restriction on z 1 can be removed when z 2 is an integer.