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analytic continuation

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1: 6.4 Analytic Continuation
§6.4 Analytic Continuation
Analytic continuation of the principal value of E 1 ( z ) yields a multi-valued function with branch points at z = 0 and z = . …
6.4.4 Ci ( z e ± π i ) = ± π i + Ci ( z ) ,
6.4.7 g ( z e ± π i ) = π i e i z + g ( z ) .
2: 28.7 Analytic Continuation of Eigenvalues
§28.7 Analytic Continuation of Eigenvalues
28.7.4 n = 0 ( b 2 n + 2 ( q ) - ( 2 n + 2 ) 2 ) = 0 .
3: 14.24 Analytic Continuation
§14.24 Analytic Continuation
4: 10.34 Analytic Continuation
§10.34 Analytic Continuation
5: 10.11 Analytic Continuation
§10.11 Analytic Continuation
6: 15.17 Mathematical Applications
By considering, as a group, all analytic transformations of a basis of solutions under analytic continuation around all paths on the Riemann sheet, we obtain the monodromy group. …
7: 16.15 Integral Representations and Integrals
These representations can be used to derive analytic continuations of the Appell functions, including convergent series expansions for large x , large y , or both. …
8: 8.2 Definitions and Basic Properties
§8.2(ii) Analytic Continuation
9: 1.10 Functions of a Complex Variable
§1.10(ii) Analytic Continuation
If f 2 ( z ) , analytic in D 2 , equals f 1 ( z ) on an arc in D = D 1 D 2 , or on just an infinite number of points with a limit point in D , then they are equal throughout D and f 2 ( z ) is called an analytic continuation of f 1 ( z ) . … Analytic continuation is a powerful aid in establishing transformations or functional equations for complex variables, because it enables the problem to be reduced to: (a) deriving the transformation (or functional equation) with real variables; followed by (b) finding the domain on which the transformed function is analytic.
Schwarz Reflection Principle
Then the value of F ( z ) at any other point is obtained by analytic continuation. …
10: 33.23 Methods of Computation
Thompson and Barnett (1985, 1986) and Thompson (2004) use combinations of series, continued fractions, and Padé-accelerated asymptotic expansions (§3.11(iv)) for the analytic continuations of Coulomb functions. …