Titlebook: Handbook of Complex Variables; Steven G. Krantz Book 1999 Springer Science+Business Media New York 1999 Argument principle.Blaschke produc

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Business Objectives vs. User Goals,have intrinsic interest. These functions are usually termed .. In this chapter we shall treat three of these which arise naturally in complex analysis: the gamma function of Euler, the beta function of Legendre, and the ζ(or zeta) function of Riemann.

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Harmonic Functions,al equation known as .:.(Of course the imaginary part y satisfies the same equation.) In this chapter we shall study systematically those . functions that satisfy this equation. They are called .. (Note that we encountered some of these ideas already in §1.4.)

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Special Functions,have intrinsic interest. These functions are usually termed .. In this chapter we shall treat three of these which arise naturally in complex analysis: the gamma function of Euler, the beta function of Legendre, and the ζ(or zeta) function of Riemann.

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Applications that Depend on Conformal Mapping,Often we take . to be a standard domain such as the disc.or the upper half plane.Particularly in the study of partial differential equations, it is important to have an . conformal mapping between the two domains. In the Appendix to this chapter we give a compendium of conformal mappings of some of the most frequently encountered planar regions.

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Book 1999hat reader who has had a course in complex analysis at some time in his life. This book is a handy com- pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.

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The Geometric Theory of Holomorphic Functions,unction is called a . (or . mapping. The fact that . is supposed to be one-to-one implies that . is nowhere zero on . [remember that if . vanishes to order . ≥ 0 at a point . ∈ ., then . is (.+1)-to-1 in a small neighborhood of P—see §§5.2.1]. As a result, h.: . . is also holomorphic—as we discussed