For example, relation between sin( x) and cos( x), series representations of the Beta function, relation between BesselJ( n, x) and AiryAi( x), differential equation for ellipticF(phi, m), and examples of complicated indefinite integrals containing erf.īut Wolfram|Alpha also knows about many special functions that are not in Mathematica because they are less common or less general. And, based on Mathematica‘s algorithmic computation capabilities and the Functions Site’s identities, most of this knowledge is now easily accessible in Wolfram|Alpha. The Wolfram Functions Site lists 300,000+ formulas and identities for these functions. All together, Mathematica knows now more than 300 such functions. Since the beginning in 1988, Mathematica knew not only elementary functions (sqrt, exp, log, etc.) but many special functions of mathematical physics (such as the Bessel function K and the Riemann Zeta function) and number theoretical functions. In this blog post, we want to report some work in progress that might interest users of probability and statistics and also those who wonder how we add new knowledge every day to Wolfram|Alpha.
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