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Diffstat (limited to 'Problem Set 1.page')
| -rw-r--r-- | Problem Set 1.page | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/Problem Set 1.page b/Problem Set 1.page index 91d2a30..91a2a40 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -14,9 +14,11 @@ - Show that the function $f(z) = z^n$ is holomorphic for any integer n (possibly negative!). How do these functions transform the complex plane? -- Show that the sum of two holomorphic functions is holomorphic; conclude that any polynomial function is holomorphic. +- Show that the sum of two holomorphic functions is holomorphic. -- Show that the product of two holomorphic functions is holomorphic. +- Show that the product of two holomorphic functions is holomorphic + +- Conclude that any polynomial function is holomorphic. - Try to extend the following functions of a real variable to holomorphic functions defined on the entire complex plane. Is it always possible to do so? What goes wrong? a. $\sinh(z), \cosh(z)$ |