Q.3 Define Beta & Gama functions and Pro ve that:
Answers
Answer:
Beta and gamma are the two most popular functions in mathematics. Gamma is a single variable function, whereas Beta is a two-variable function. The relation between beta and gamma function will help to solve many problems in physics and mathematics.
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Beta Functions
The beta function is a unique function where it is classified as the first kind of Euler’s integral. The beta function is defined in the domains of real numbers. The notation to represent the beta function is “β”. The beta function is meant by B(p, q), where the parameters p and q should be real numbers.
The beta function in Mathematics explains the association between the set of inputs and the outputs. Each input value the beta function is strongly associated with one output value. The beta function plays a major role in many mathematical operations.
Gama Functions
The gamma distribution term is mostly used as a distribution which is defined as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions. It is related to the normal distribution, exponential distribution, chi-squared distribution and Erlang distribution. ‘Γ’ denotes the gamma function.