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In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by

for Re(x), Re(y) > 0. The beta function is symmetric, meaning that

It has many other forms, including:

where (x)_n is the falling factorial. Euler's Beta function was the first known scattering amplitude in string theory, first conjectured by Gabriele Veneziano .

See also

• binomial coefficient
• Euler integral
• falling factorial
• gamma function
• incomplete beta function