If we have trial functions, which depend on n, of the form 6,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: too dxó, (x)x² óm(x) = dra"+m+Pexp(-2ax²). (3) To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: rtoo I (2a) = | ) = / dez*erp{-2ar") (4) 1. If u = x2k-1 what is du? 2. If dv = xexp(-2ax²)dx, what is v? 3. What is the value of uv at x = 0? What is the value of uv at x = -oo? 4. What is the value of I-1(2a) in terms of I(2a)? k I(2a) (m,p,n) 1 2 TABLE I. Complete the table above by filling in the value of I(20)
If we have trial functions, which depend on n, of the form 6,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: too dxó, (x)x² óm(x) = dra"+m+Pexp(-2ax²). (3) To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: rtoo I (2a) = | ) = / dez*erp{-2ar") (4) 1. If u = x2k-1 what is du? 2. If dv = xexp(-2ax²)dx, what is v? 3. What is the value of uv at x = 0? What is the value of uv at x = -oo? 4. What is the value of I-1(2a) in terms of I(2a)? k I(2a) (m,p,n) 1 2 TABLE I. Complete the table above by filling in the value of I(20)
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