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Let ##g(x,t)=\int f(k,x,t)\,dk##
Under what conditions is the following true?
##g(x,0)=\int f(k,x,0)\,dk##
That is, we can get the value of ##g(x,t)## when ##t=0##, by
(1) either substituting ##t=0## into ##g(x,t)## or
(2) by first substituting ##t=0## into ##f(k,x,t)## and then integrating wrt ##k##.
Does it work for non-zero values of ##t##?
EDIT: ##g(x,t)=\int f(x,t)\,dx## corrected to ##g(x,t)=\int f(k,x,t)\,dk##.
Under what conditions is the following true?
##g(x,0)=\int f(k,x,0)\,dk##
That is, we can get the value of ##g(x,t)## when ##t=0##, by
(1) either substituting ##t=0## into ##g(x,t)## or
(2) by first substituting ##t=0## into ##f(k,x,t)## and then integrating wrt ##k##.
Does it work for non-zero values of ##t##?
EDIT: ##g(x,t)=\int f(x,t)\,dx## corrected to ##g(x,t)=\int f(k,x,t)\,dk##.
Last edited: