PSI Lectures/Special Functions and Distributions

Lecture 1 - Dirac delta; Test functions; Distributions and their derivatives.
Lecture 2 - Orthogonal polynomials; Recurrence relations; Weights.
Lecture 3 - Generalized Rodrigues' formulae; Classification of orthogonal polynomials; Sturm-Liouville theory.
Lecture 4 - Gamma; Zeta; Hypergeometric functions

Lecture 1 - Distributions: test functions, Dirac delta function, Derivatives of distributions, Multiplication of distributions by functions
Lecture 2 - Solution Methods: Reduction of order, Variation of parameters, Power series method, WKB approximation
Lecture 3 - Orthogonal Functions - Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials
Lecture 4 - Special Functions and Complex Variables: Gamma function, Stirling's approxximation, Saddle point method, Zeta function

Lecture 1 - Distribuitions, Test functions, Derivatives of distributions, Multiplication of distributions with functions
Lecture 2 - Composition of distributions with functions, Orthogonal functions, Sturm-Liouville theory, Parseval's Theorem, Orthogonal polynomials
Lecture 3 - Orthogonal polynomials, gamma function, Zeta function, Hypergeometric functions
Lecture 4 - Asymptotic Series, Stirling's approximation, Saddle point method

Lecture 1: Distributions, Test functions, Derivatives of distributions
Lecture 2: Multiplication of distributions with functions, Composition of distributions with functions, Functional derivatives, Gamma, Zeta
Lecture 3: Orthogonal functions, Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials
Lecture 4: Asymptotic series, Stirling's approximation, Saddle-point method

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