Beta Function Last Updated : 16 Jun, 2020 Improve Improve Like Article Like Save Share Report The Beta function is a unique function and is also called the first kind of Euler’s integrals. The beta function is defined in the domains of real numbers. The notation to represent it is “β”. The beta function is denoted by β(p, q), Where the parameters p and q should be real numbers. It 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. Beta function is defined by- where p>0 and q>0 Some standard results: Symmetry : Put x=1-y Beta function in terms of trigonometric functions : Beta function expressed as improper integral : Relation between beta and gamma functions : where 0<p<1 if p is an even positive integer if p is an odd positive integer for m, n positive integers Example-1: Evaluate Explanation : Using result (4) we get, We know that Thus we get =0.1964 Example-2: Evaluate Explanation : As p=10 is a positive integer, using result (8(i)) we get, Example-3: Evaluate Explanation : As p=9 is an odd positive integer, using result 8(ii) we get, Like Article Suggest improvement Previous Integrals Next Gamma Function Share your thoughts in the comments Add Your Comment Please Login to comment...