Schwarz reflection principle

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21—30 of 51 matching pages

21: 10.74 Methods of Computation

… ►To ensure that no zeros are overlooked, standard tools are the phase principle and Rouché’s theorem; see §1.10(iv). …

22: 27.10 Periodic Number-Theoretic Functions

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23: Bibliography R

… ►

W. Rudin (1976) Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.

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Notes:: International Series in Pure and Applied Mathematics
External Links:: MathReview, ZentralBlatt
Referenced by:: §1.4(iii).
Encodings:: BibTeX

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24: 18.38 Mathematical Applications

… ►The Dunkl operator, introduced by Dunkl (1989), is an operator associated with reflection groups or root systems which has terms involving first order partial derivatives and reflection terms. … ►The Dunkl type operator is a

q

-difference-reflection operator acting on Laurent polynomials and its eigenfunctions, the nonsymmetric Askey–Wilson polynomials, are linear combinations of the symmetric Laurent polynomial

R_{n}(z;a,b,c,d\,|\,q)

and the ‘anti-symmetric’ Laurent polynomial

z^{-1}(1-az)(1-bz)R_{n-1}(z;qa,qb,c,d\,|\,q)

, where

R_{n}(z)

is given in (18.28.1_5). …

25: 10.47 Definitions and Basic Properties

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§10.47(v) Reflection Formulas

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26: 31.8 Solutions via Quadratures

… ►The curve

\Gamma

reflects the finite-gap property of Equation (31.2.1) when the exponent parameters satisfy (31.8.1) for

m_{j}\in\mathbb{Z}

. …

27: 28.5 Second Solutions $\operatorname{fe}_{n}$ , $\operatorname{ge}_{n}$

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S_{2m+2}(-q)=S_{2m+2}(q).

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28: 35.7 Gaussian Hypergeometric Function of Matrix Argument

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Reflection Formula

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29: 4.23 Inverse Trigonometric Functions

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§4.23(iii) Reflection Formulas

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30: 26.9 Integer Partitions: Restricted Number and Part Size

… ►The conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots. …