InterviewSolution
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InterviewSolution
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If m gt 0, n gt 0, the definite integral l=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx depends upon the vlaues of m and n and is denoted by beta(m,n), called the beta function. E.g. int_(0)^(1)x^(4)(1-x)^(5)dx=int_(0)^(1)x^(5-1)(1-x)^(6-1)dx=beta(5, 6) and int_(0)^(1)x^(5//2)(1-x)^(-1//2)dx=int_(0)^(1)x^(7//2-1)(1-x)^(1//2-1)dx=beta((7)/(2),(1)/(2)). Obviously, beta(n, m)=beta(m, n). If int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dx, then k is equal to |
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Answer» `(m)/(N)` |
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