- Docente: Daniele Ritelli
- Credits: 3
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Quantitative Finance (cod. 6692)
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from Sep 18, 2026 to Oct 16, 2026
Learning outcomes
Acquire basic knowledge of the theory of analytic functions of a complex variable and Eulerian and hypergeometric functions.
Course contents
Algebraic, geometric, and topological properties of the set of complex numbers.
Holomorphic functions: Cauchy-Riemann conditions. Power series, integer functions, analytic functions. Exponential and elementary functions in the complex field. Integral over complex paths: Cauchy integral formula. Residue theorem and its application to the computation of real integrals. Gamma and Beta functions: error function, probability integral, reflection formula, Euler and Gauss infinite products for Gamma. Hypergeometric function Application to Beta and Gamma random variables.
Partial differential equations: heat equation integrated by the Fourier transform. Parabolic equations with constant coefficients. Linear parabolic Euler-Cauchy equations.
Readings/Bibliography
Daniele Ritelli
Introduction to Special Functions for Applied Mathematics
ISBN 9780367774691
2025 Chapman and Hall/CRC
Cap. 1 tranne 1.10
Cap. 2
Daniele Ritelli, Giulia Spaletta
Introductory Mathematical Analysis for Quantitative Finance
ISBN 9781351245111
2020 Chapman and Hall/CRC
Cap. 5 sect- 1
Cap 12-13
Teaching methods
Ex cathedra lectures on tablets, recorded and available at the end of the class.
Assessment methods
Learning is assessed through a two-hour written test. It aims to assess the student's acquired problem-solving skills related to the topics covered in class.
The proficiency test consists of detailed solutions in Italian for three exercises. Proficiency is achieved if at least one of the exercises is set up correctly.
AI can be a useful tool to assist individual study with in-depth analysis, summaries and self-assessment paths, however, the use of AI during exams is prohibited. Any use constitutes a violation of academic integrity.
Teaching tools
Downloadable teaching materials
Video projection. Blackboard. Computer Algebra will be used to illustrate relevant topics.
Learning materials presented in class will be made available to students in electronic format.
Office hours may also be held via Teams.
The instructor responds to signed emails containing the student's name, surname, and student ID number regarding appointment requests, explanations, and information not already available on the website.
Links to further information
Office hours
See the website of Daniele Ritelli
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.