Residues on Beta Function

Abstract

The Beta function is part of a special function in the form of an integral statement and the result form is twice the multiplication of factorial functions. The Beta function is part of an unnatural integral because it has infinite-value parameters, resulting in infinite functions. Beta function is symbolized as β which basically can be defined in real and complex numbers with certain conditions. Completion of Beta functions can use residues. Residue is the residual product of an equation that has a singular point. Residues are used in calculating the integration of complex functions on unnatural integrals. Then the residue can complete the Beta function. Residues in the Beta function use the analysis of the concept of residues by determining the convergence, analytical, and kesingularitas areas of the Beta function, a Beta function domain is obtained. The domain area can be used in expanding the Laurent series. Then you will get a pole or pole that will affect the calculation in obtaining residuals. Based on the results of the study, the Beta function has a singular point that causes the point is not analytic to the Beta function. The singular point occurs at the point , then the residual form in the Beta function with the n-level pole and the singular point  forms the equation,

(  

dengan .

and the parameter value  contains infinite positive integers, then for each positive integer value entered in the Beta function produces a zero value residue.

Keywords: Beta function, residue