-
Title: Application of the Identity Theorem
-
Series: Complex Analysis
-
YouTube-Title: Complex Analysis 31 | Application of the Identity Theorem
-
Bright video: https://youtu.be/rsYF_OHo__8
-
Dark video: https://youtu.be/SwynIS_9SvI
-
Ad-free video: Watch Vimeo video
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: ca31_sub_eng.srt missing
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $f: \mathbb{C} \rightarrow \mathbb{C}$ be a holomorphic function given by $f(x) = \cos(x)$ for all $x \in \mathbb{R}$. What is correct?
A1: For all $z \in \mathbb{C}$, we have $f(z) = \sum_{j=0}^\infty \frac{(-1)^j}{(2j)!} z^{2j}$.
A2: For all $z \in \mathbb{C}$, we have $f(z) = \sum_{j=0}^\infty \frac{(-1)^j}{(2j+1)!} z^{2j+1}$.
A3: There are infinitely many functions $f$ that satisfy the conditions.
A4: There are exactly two functions $f$ that satisfy the conditions.
Q2: Let $f: \mathbb{R}\rightarrow \mathbb{R}$ be a $C^\infty$-function. What is correct?
A1: There is at most one function $g: \mathbb{C} \rightarrow \mathbb{C}$ that is holomorphic and satisfies $g(x) = f(x)$ for all $x \in \mathbb{R}$.
A2: There is at most one function $g: \mathbb{C} \rightarrow \mathbb{C}$ that satisfies $g(x) = f(x)$ for all $x \in \mathbb{R}$.
A3: There are two holomorphic functions $g: \mathbb{C} \rightarrow \mathbb{C}$ that satisfy $g(x) = f(x)$ for all $x \in \mathbb{R}$.
-
Last update: 2024-10
