Transcription of Beta Function and its Applications
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Beta Function and its Applications
Beta Function and its ApplicationsRiddhi D.~Department of Physics and AstronomyThe University of TennesseeKnoxville, TN 37919, USAA bstractThe Beta Function was rst studied by Euler andLegendre and was given its name by Jacques as the gamma Function for integers describes fac-torials, the beta Function can de ne a binomial coe -cient after adjusting beta Function was the rst known scattering amplitude in string theory, rstconjectured by Gabriele Veneziano. It also occursin the theory of the preferential attachment process,a type of stochastic urn incomplete betafunction is a generalization of the beta Function thatreplaces the de nite integral of the beta Function withan inde nite situation is analogous to theincomplete gamma Function being a generalization ofthe gamma IntroductionThe beta Function (p;q)is the name used by Legen-dre and Whittaker and Watson(1990) for the betaintegral (also called the Eulerian integral of the rstkind). It is de ned by (p;q) =(p 1)!
Beta Function and its Applications Riddhi D. ~Department of Physics and Astronomy The University of Tennessee Knoxville, TN 37919, USA Abstract The Beta function was –rst studied by Euler and
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