Course on special functions
The course on Special Functions by
Tom H. Koornwinder and
Raimundas Vidunas
at Universiteit van Amsterdam during SeptemberNovember 2000
will be given in a less intensive form than
earlier announced in the "studiegids" because only few
students registered for this course.
Participants will study themselves selected parts
from the book
N.M. Temme,
"Special functions, an introduction to the classical functions
of mathematical physics", Wiley, 1996,
and from some further material.
A twohour session will be held once a week on
Wednesday, 15.1517.00 hour in room P.014 of the Euclides building.
During the first hour difficulties met while
reading the book will be explained. During the second hour participants
will present solutions of exercises on the blackboard which have been
assigned to them one week in advance.
Tentative list of subjects:
 Chapter 2: Gamma function
 Section 4.2: Differential equations in the complex plane
 Chapter 5: Hypergeometric functions
 Chapter 6: Orthogonal polynomials
 Chapter 9: Bessel functions
 not from the book: qHypergeometric functions
Audience and examen:
The course is suitable for 4th year (and possibly 3rd year) undergraduate
students and for beginning graduate students in mathematics and in
(theoretical) physics. Marks (7 "studiepunten") can be obtained by
submitting takehome exercises or a longer paper or after an oral examination
or by a combination of these.
Schedule:

September 13:
Definite arrangements of the course were discussed

September 20:
Ch. 3, Gamma functions, pp.4156 (theory) and Exercises 3.3 and 3.73.13.

September 27:
Section 2.2.1 (Watson's Lemma), Section 3.6 (asymptotics of gamma function),
Section 3.6.2 (asymptotics of ratio of two gamma functions);
Exercises 3.17, 3.18.

October 4:
Sections 4.2, 4.2.1, 4.2.2, 4.2.4, 4.2.5, 4.2.5.1;
Exercises 4.3, 4.4, 4.6.
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