- #1
Bazman
- 21
- 0
Hi,
i've seen a textbook where the integration inthe following expression is performed:
C(S,V,t) = 1-(1/2pi)*exp[-lambda(k0)*t](u(k0,V)/k0^2-i*k0)
+ infin
*S exp[-.5*kr^2*lambda''(k0)*t]dkr
- infin
where kr is k subscript r and k0 is ksubscript 0
i = complex number
lamda'' =2nd derivative of lambda
giving
=1-(u(k0,V)/(k0^2-i*k0)*(1/(2pi*lamda''(k0)*t)^.5)*exp[-lambda(k0)*t]
to me the integral
+ infin
*S exp[-.5kr^2*lambda''(k0)t]dkr
- infin
should give exp[-.5kr^2lambda''(k0)*t]/(-kr*lambda''(k0)*t)
evaluated at + and - infin and in both cases should go to zero but from the solution above this is clearly incorrect
please let me know where I am going wrong
i've seen a textbook where the integration inthe following expression is performed:
C(S,V,t) = 1-(1/2pi)*exp[-lambda(k0)*t](u(k0,V)/k0^2-i*k0)
+ infin
*S exp[-.5*kr^2*lambda''(k0)*t]dkr
- infin
where kr is k subscript r and k0 is ksubscript 0
i = complex number
lamda'' =2nd derivative of lambda
giving
=1-(u(k0,V)/(k0^2-i*k0)*(1/(2pi*lamda''(k0)*t)^.5)*exp[-lambda(k0)*t]
to me the integral
+ infin
*S exp[-.5kr^2*lambda''(k0)t]dkr
- infin
should give exp[-.5kr^2lambda''(k0)*t]/(-kr*lambda''(k0)*t)
evaluated at + and - infin and in both cases should go to zero but from the solution above this is clearly incorrect
please let me know where I am going wrong