This script can be pasted into the Eigenmath app.

 -- Feynman and Hibbs problem 3-9 -- Tba is tb - ta -- Tbc is tb - tc -- Tca is tc - ta Tba = Tbc + Tca "Verify equations (5), (6), and (7)" D = i m (xb - xc)^2 / (2 hbar Tbc) + i (xb + xc) Tbc f / (2 hbar) + i m (xc - xa)^2 / (2 hbar Tca) + i (xc + xa) Tca f / (2 hbar) A = i m (1 / Tbc + 1 / Tca) / (2 hbar) B = i f Tba / (2 hbar) - i m (xb / Tbc + xa / Tca) / hbar C = i f (xb Tbc + xa Tca) / (2 hbar) + i m (xb^2 / Tbc + xa^2 / Tca) / (2 hbar) check(D == A xc^2 + B xc + C) "ok" "Verify equation (8) solution of integral" check(-pi / A == -2 pi hbar Tbc Tca / (i m Tba)) D = -B^2 / (4 A) + C A = i m (xb - xa)^2 / (2 hbar Tba) B = i f Tba (xb + xa) / (2 hbar) C = -i f^2 Tba Tbc Tca / (8 hbar m) check(D == A + B + C) "ok" "Verify equation (10) complete the cube" A = (tb - ta)^3 B = (tb - tc)^3 + (tc - ta)^3 + 3 (tb - ta) (tb - tc) (tc - ta) check(A == B) "ok" "Verify equation (12) combine exponentials" A = -(tb - tc)^3 / (24 hbar m) B = -(tc - ta)^3 / (24 hbar m) C = -(tb - ta) (tb - tc) (tc - ta) / (8 hbar m) D = -(tb - ta)^3 / (24 hbar m) check(A + B + C == D) "ok" "Verify equation (14) cancellation of coefficients" D = m / (2 pi i hbar Tba) A = m / (2 pi i hbar Tbc) B = m / (2 pi i hbar Tca) C = -2 pi hbar Tbc Tca / (i m Tba) check(sqrt(D) == sqrt(A B C)) "ok"