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dxa"+m+Pexp(-2ax²). %3D 1. Explain in your own words what the terminology for each of the quantities in above expression is. 2. When k=n+m+p is an odd number, what can you say about the integral?

dxa"+m+Pexp(-2ax²). %3D 1. Explain in your own words what the terminology for each of the quantities in above expression is. 2. When k=n+m+p is an odd number, what can you say about the integral?

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dro,(x)x® Óm(x) =| d If we have trial functions, which depend on n, of the form ø,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: +oo dxr"+m+Pexp(-2ax²). (3) 1. Explain in your own words what the terminology for each of the quantities in the above expression is. 2. When k=n+m+p is an odd number, what can you say about the integral? To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: etoo I (2a) = | ) = [** dzz*ecxp(-2ax²) (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 |(612*l61) = (øo]a*l60) = ($2\a²\&2) = (ø4|04) TABLE I. Complete the table above by filling in the value of Ik(2a)
Transcribed Image Text:dro,(x)x® Óm(x) =| d If we have trial functions, which depend on n, of the form ø,n = x"exp(-ax). We are interested in being able to perform integrals (for any values of n, m and p) of the form: +oo dxr"+m+Pexp(-2ax²). (3) 1. Explain in your own words what the terminology for each of the quantities in the above expression is. 2. When k=n+m+p is an odd number, what can you say about the integral? To perform these integrations we introduce the following integral and then employ integra- tion by parts to develop a recursion relation: etoo I (2a) = | ) = [** dzz*ecxp(-2ax²) (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 |(612*l61) = (øo]a*l60) = ($2\a²\&2) = (ø4|04) TABLE I. Complete the table above by filling in the value of Ik(2a)
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