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1. Reduction Formulae 2. Beta function 3.
Gamma functionReduction Formulae are recursive mathematical expressions that help evaluate integrals by reducing them to simpler forms, often in terms of lower powers or smaller expressions. A reduction formula is typically derived using integration by parts or recursion techniques and is useful when dealing with integrals involving powers of trigonometric, exponential, or polynomial functions. The Beta function, denoted as B(m,n)B(m, n)B(m,n), is a special function.
It is a symmetric function, meaning:B(m,n)=B(n,m). B(m, n) = B(n, m). B(m,n)=B(n,m).
Applications of Beta FunctionUsed in probability theory (Beta distribution). Appears in combinatorics and statistics. Integral evaluations in physics and engineering.
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