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In an upcoming paper, Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we establish several integration by parts formulas involving generalized Feynman integrals, generalized Fourier-Feynman transforms, and the first variation of functionals of the form F(x) = f( ,..., ) where denotes the Paley-Wiener-Zygmund stochastic integral ∫ T 0 α(t)dx(t).

Integration by parts formulas involving generalized Fourier-Feynman transforms on function space