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Sir i have a boubt in laplace transformations that is L{t^(-1/2)} is possible or not? if possible what is the answer? if not why?

Sir i have a boubt in laplace transformations that is L{t^(-1/2)} is possible or not? if possible what is the answer? if not why?
 

Grade:12th pass

2 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
Using L{t^(n-1/2)} = (2n-1)!root(pi)/2^ns^(n+1/2).
L{t^1/2} = 1.root(pi)/root(s).
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Nandana
110 Points
3 years ago
hi !
   you can solve this by using Gamma function
here,
      F(s) =2∫0+infinete t-1/2  e-st dt    [If dual Laplace transform]
             take,
               st =x
               dt = x/s
           = 2 s∫0+infinete (x/s)-1/2  e-x dx
           = 2/√s∫0+infinete (x)-1/2  e-x dx
           =2/√s  Gamma(1/2)
           =2√pi/√s
      If you are thinking about single side Laplace Transform , the answer is
                 √pi /√s                                  
                                         Thank you !
                                          good luck …

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