Lectures related to Incomplete gamma function

Analytical Extension of Gamma Function

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

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Bessel Equation: First Frobenius Series Solution around x=0

Explores the Bessel equation solution method and the gamma function properties.

Gamma Function and Stirling's Approximation: Mathematical Methods

Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.

Bessel Equation: Second Frobenius Series Solution

Explores the Bessel equation, deriving solutions and investigating the existence of a second Frobenius series solution.

Real Functions: Definitions and Examples

Explores definitions and examples of real functions of a real variable.

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Stirling's Formula and Functional Equation for Zeta

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Linear Equation Solution Example

Illustrates the resolution of a linear equation with a second member.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Gamma function II, and Poisson summation formula

Covers the Gamma function properties and the Poisson summation formula for real and complex numbers.

Boolean Algebra: Properties and Optimization

Covers Boolean algebra properties, optimization techniques, and the importance of valid groups in Karnaugh maps.

Non-vanishing of Dirichlet L-function and Gamma functions

Covers the proof of non-vanishing of Quadratic Dirichlet L-function and reviews basic properties of Gamma function.

Functions: Parametric, Integrals, Multi-variable

Covers parametric functions, integrals, and the origin of plasticity in metals.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.