Changes between Initial Version and Version 1 of Ticket #24006, comment 19


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Timestamp:
10/16/17 16:53:27 (2 years ago)
Author:
charpent
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  • Ticket #24006, comment 19

    initial v1  
    1010An example of possible usefulness :
    1111{{{
    12 sage: dgamma(y,y,theta)=y^(k-1)*e^(-y/theta)/(theta^k*gamma(k))
     12sage: dgamma(y,k,theta)=y^(k-1)*e^(-y/theta)/(theta^k*gamma(k))
    1313sage: (dgamma(y,k,theta).laplace(y,x)^p).expand().canonicalize_radical().inverse
    1414....: _laplace(x,y)
    15 ilt(k^((k - 1)*p)*theta^(-k*p)*gamma(k)^(-p)*e^(-k*p/theta)/x^p, x, y)
     15ilt(1/((theta*x + 1)^(k*p)), x, y)
    1616sage: sympy.inverse_laplace_transform((dgamma(y,k,theta).laplace(y,x)^p).expand(
    1717....: ).canonicalize_radical(),x,y)._sage_()
    18 k^((k - 1)*p)*theta^(-k*p)*y^(p - 1)*(gamma(k + 1)/k)^(-p)*e^(-k*p/theta)*heaviside(y)/gamma(p)
     18k*p*theta^(-k*p)*y^(k*p - 1)*e^(-y/theta)*heaviside(y)/gamma(k*p + 1)
    1919}}}
    2020