Hendriks, W.H. (2009) The SchwarzChristoffel transformation and elliptic functions. Bachelor's Thesis, Mathematics.

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Abstract
An important result from complex analysis, the Riemann mapping theorem, states that there exists a conformal bijective mapping f, from A to B between any two simply connected open sets A and B, both not equal to the whole complexplane C. In the case where the upper halfplane is conformally mapped onto an open set which is the inside of a simple polygon, the mapping has the form of a SchwarzChristoffel transformation (SCT). The SCT will be discussed in detail, and will be used to define Jacobi elliptic functions. Jacobi elliptic functions form a special set of elliptic functions in general. Elliptic functions are doubly periodic meromorphic functions. Basic properties of elliptic functions will be discussed.
Item Type:  Thesis (Bachelor's Thesis) 

Degree programme:  Mathematics 
Thesis type:  Bachelor's Thesis 
Language:  English 
Date Deposited:  15 Feb 2018 07:29 
Last Modified:  15 Feb 2018 07:29 
URI:  http://fse.studenttheses.ub.rug.nl/id/eprint/8760 
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