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Sep 22, 2016 · 3 an infinite number of integrals, (because goes to zero, of course) of exponential (iS / ) where S is the action expression (3), S L(x ,x)dt (3) At last, I had succeeded in representing quantum mechanics directly in terms of the



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( t)n = 1 2 X1 n=0 ˚(n)(0) n (1 + ( 1)n)t2 = X1 n=0 ˚(2n)(0) (2n) t2n; which gives us ˚ even(p s) ˘ X1 n=0 ˚(2n)(0) (2n) sn: The integral (2 9) is now suitable for using Watson’s lemma and we observe that ˙= 1=2 and T= 2 Thus we obtain the asymptotic expansion F( ) ˘ X1 n=0 ˚(2n)(0)( n+ 1=2) (2n) n+1=2 (2 10) as 1



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On est bien ramené au calcul d'une primitive de la fonction rationnelle S(t) = R 2t 1+t2 1−t2 1+t2 2 1+t2 2- Règles de Bioche : Cependant, dans certains cas, on peut utiliser un changement de ariablev qui donne des calculs moins



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(t ) n + 1 d ,for(n 1 < < n ) (10) In this chapter we will consider mainly the GL, the RL, and the Caputo de nitions This consideration is based on the fact that, for a wide class of functions, the three best known de nitions - GL, RL, and Caputo - are equivalent under some conditions (Podlubny, 1999)



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Tn = 1 3 Comme les deux suites encadrent A, on a : A = 1 3 u a et donc Z 1 0 x2 dx = 1 3 Calculette TI 82 :Pour calculer la valeur exacte de cette intégrale faire (dans le menu math) fonctIntégr(X2,X,0,1)⊲Frac on retrouve 1/3 PAUL MILAN 4 TERMINALE S



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7 1 Introduction to the Laplace Method 247 Laplace Integral The integral R1 0 g(t)est dt is called the Laplace integral of the function g(t) It is de ned by limN1 RN 0 g(t)est dt and



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t N − 1) x N − 1 x N − 1 × x 2 1 x e iH (t 2 − t 1) x x 1 x 1 x 1 e − iH (T + t 1) S x 0 (6 16) Thus, we see that the path integral is so smart that it can even calculate the ground state wave function for us The last matrix element in Eq (6 16) can also be written as x 1 0 e iH (t 1 − (−)) t x 0, which can be described as

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