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# Lecture 5: Exercises

### Suggestions for further reading

- Taylor expansion: Arfken (chap. 5.6)

### Questions for Review

- How is the Gamma function defined? What is its value for
natural arguments?
- How is the Riemann Zeta function defined?
- What is a Taylor series? How do you calculate its coefficients?
- What is a Maclaurin series?
- Do all functions have a Taylor expansion? Give examples!
- What is the binomial theorem?
- Give the Taylor expansions of the following functions:
- exp(x)
- sin(x), cos(x)
- ln(1+x), ln(1-x)
- 1/(1-x)

- How can one extend functions like sin, cos, exp,.. into the
complex plane?

### Problems