- #1
navaneethkm
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I am graduate student in engineering. In course of my research I have encountered an integral of this form
##\int_{t'}^{t} e ^{-b t_1} dt_1 \int_{t'}^{t_1 } e ^{b t_2} dt_2 \int_{t'}^{t_2 } e ^{-b t_3} dt_3 \int_{t'}^{t_3} e ^{b t_4} dt_4 ... \int_{t'}^{t_{n-1}} e ^{b t_n} dt_n ##
I am trying to find a general form of the result of this integral. Can someone give some pointers on how to solve this integral.Are there problems in physics especially related to translational Brownian motion where one encounters such integrals?
While writing this integral I have assumed t>t1>t2>...>tn>t' .
##\int_{t'}^{t} e ^{-b t_1} dt_1 \int_{t'}^{t_1 } e ^{b t_2} dt_2 \int_{t'}^{t_2 } e ^{-b t_3} dt_3 \int_{t'}^{t_3} e ^{b t_4} dt_4 ... \int_{t'}^{t_{n-1}} e ^{b t_n} dt_n ##
I am trying to find a general form of the result of this integral. Can someone give some pointers on how to solve this integral.Are there problems in physics especially related to translational Brownian motion where one encounters such integrals?
While writing this integral I have assumed t>t1>t2>...>tn>t' .