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Mathematics Calculus Wolfram Language

Obtain the conversion of Gamma function?

Jacques Ou

Posted 6 years ago

POSTED BY: Jacques Ou

3 Replies

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J. M.

Posted 6 years ago

POSTED BY: J. M.

Jim Baldwin

Posted 6 years ago

I would think that you want to have a conversion that doesn't require you to know the specific `Gamma` coefficients. Does the following do what you want? eq1 = F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)]) FullSimplify[eq1] /. Gamma[a_, b_] - Gamma[a_, c_] -> Gamma[a, b, c] (* F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T), R0^2/(4 T)]) *)

I would think that you want to have a conversion that doesn't require you to know the specific Gamma coefficients. Does the following do what you want?

eq1 = F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 
     2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)])

FullSimplify[eq1] /. Gamma[a_, b_] - Gamma[a_, c_] -> Gamma[a, b, c]

(* F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) + 
    2^-Rv Gamma[-(Rv/2), Rx^2/(4 T), R0^2/(4 T)]) *)

POSTED BY: Jim Baldwin

Jacques Ou

Posted 6 years ago

Yes, Your codes are what I wanted. Actually it also works with the coefficient. In[88]:= eq1 = F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)]) Out[88]= F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)]) In[89]:= eq2 = eq1 /. {2^-Rv Gamma[a_, b_] - 2^-Rv Gamma[a_, c_] -> 2^-Rv Gamma[a, b, c]} Out[89]= F1[1][T] == E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) + 2^-Rv Gamma[-(Rv/2), Rx^2/(4 T), R0^2/(4 T)])

Yes, Your codes are what I wanted. Actually it also works with the coefficient.

In[88]:= eq1 = 
 F1[1][T] == 
  E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 
     2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 
     2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)])

Out[88]= F1[1][T] == 
 E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) - 
    2^-Rv Gamma[-(Rv/2), R0^2/(4 T)] + 
    2^-Rv Gamma[-(Rv/2), Rx^2/(4 T)])

In[89]:= eq2 = 
 eq1 /. {2^-Rv  Gamma[a_, b_] - 2^-Rv  Gamma[a_, c_] -> 
    2^-Rv Gamma[a, b, c]}

Out[89]= F1[1][T] == 
 E^-T B1[1] (-((2 E^(-(Rx^2/(4 T))) (Rx^2/T)^(-Rv/2))/Rv) + 
    2^-Rv Gamma[-(Rv/2), Rx^2/(4 T), R0^2/(4 T)])

POSTED BY: Jacques Ou

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