Property of Beta Function|| Beta Function #Gammafunction#relationBetaandGamma#beta#Gamma#Function

The Riemann-Stieltjes Integrals: Definition and existence of integrals. Properties of
integrals. Fundamental theorem of calculus and its applications. Change of variable
theorem. Integration by parts.
Functions of Bounded Variation: Definition and examples. Properties of functions
of bounded variation.
Improper Integrals: Types of improper integrals. Tests for convergence of improper
integrals. Beta and gamma functions. Absolute and conditional convergence of
improper integrals.
Sequences and Series of Functions: Definitions and examples of point-wise and uniform convergence.
Uniform convergence and continuity. Uniform convergence and integration. Uniform convergence and
differentiation. Series of functions. The Weierstrass M-test, Power series.

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