t t m = n = 0 K m,n = 0 m = n 0 K m,n = (mt) (nt) dt = 1 2 (m + n)t dt 1 2 (2mt) dt = 0 K m,n = (mt) dt = 1 2

Dimension: px

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Download "t t m = n = 0 K m,n = 0 m = n 0 K m,n = (mt) (nt) dt = 1 2 (m + n)t dt 1 2 (2mt) dt = 0 K m,n = (mt) dt = 1 2"

Germain Germain
il y a 5 ans
Total affichages :

1 t 6 e3t t 3( t) 3 t t t 3 ( + t3 ) t ( + t) t t t t t t ( t) t t t e et t ( t) t t m I m, π m I m, m m J m, m I m, π π (mt) (mt) (t) J m, m J m, π π π (mt) (mt) (t) π π ( + (mt)) π (m + )t + π π ( (mt)) π (m )t π (m )t (m + )t m K m, m m K m, π (mt) K m, π (mt) (t) π (m + )t π (m )t

2 I J π/ K [ ] π/ + e / î e /ó π/ ( e ), ( ) + î ó + [ ] π/ B A 4 (/) [ ( )] π 6 B π π ( ) B B π π 4 4 π ( ( ) ) ï + ò π 3 ( ) ( ) 3 π π ( ( ) ) e i e i 3 i e 3i 3e i + 3e i e 3i 8i ( (3) + 3 ) ò π Å ï (3) 3 3 C t t t C π π π t t t [ t t ] π» ( t) t t + π ( t) t ( ( t) ) t π C C π 4. [, π ] t ( t)

3 C C [ ] Å C + [ ] C + π C π 4. C y + y C C π 4 f() f e i e i 3 e i3 + e i3 i (ei6 e i6 3e i + 3e i )(e i3 + e i3 ) 6i ei9 e i9 3(e i5 e i5 ) + e i3 e i3 + 3(e i e i ) 6i 8 (9) (5) 3 8 () 8 (3). F() 7 (9) 3 4 (5) () + 4 (3). e () 3 i e i 3 ei6 e i6 3(e i 3e i ) i 4 i 4 (6) (). π/ π/ () 3 ï 4 (6) 3 ò π/ 8 (). π/

4 [, ] f() ( t) + (t ) / + ( ) / + / f() f() (t ) + / ( t) / u (t) + u I + u u () ( + ) J Å d + ( ()) u e K () Å π e + u u + u + u + u L u + u u + u + u Å π 4 u + u + 3 t ( 3 3) u () M π/4 d () Å + / / / u Å + ( + )

5 u () N π/3 π/4 u () O π/ d / () / u Å + (3) ( + ) ( 3) () 3 ()d /3 /5 5 u ( u ) u () (u) π/4 () O + () d 3 + u (4/3) O π/4 u /4 O 4 + d 4 + /4 d 4 + π/4 (u) ( (u)) π (u 3 + u u ) + u 5 + u 4 u + 4(/4 + /3 / ) + () + π 3 + () + π u u u + z α + i H() ( e i z ) + z ( φ) + α + ( φ) + φ z H α [, ] + α + 4 α + α 3 α 3 H α < 3

6 H F() F H F C ] π, π[ F() α t + t + u t t t C [, ] [, ] t t u F() ( + u ) Ä α u + u + ä +u +u ( α)u + u + + α α α < 3 F() α α < 3 3 α > β 3α α F() α 3 α u + α u + +α α Ä ä u + α + β α β Å α 3 α + 3 α Å α Ä ä u + α + 3α (α) Å Å Å β + Å α β Å 3 α α π H F(π) π π H(t) π π F(π) F(π) F(π) F F(π) H(t) + F() ] π, π[ F(π) F(π) F(π) π 3 α F() π f R R R R F() + f(t) t R α + α + β t α R + + F() F() + α α ] π, [ π C [, ] [, ] u t f t + t Å F() ( + t ) Ä ä α + β +t αt + α + β α α(α + β) α + β α 4 β 45 f π π π π ( π ) I f(t) f(t) 4 f(t) 4F π

7 F f R R π I ( π ) Å F π α(α + β) π π π α(α + β) 4(4 + 45) 7 α α + β π α(α + β) a b a +b + b a θ π a + b I + b a Å b a θ ( + θ)( θ) b a θ dθ π π a + b + b a b a θ θ θ dθ b a π b a π a + b + b a [ θ θ dθ θ θ π π, π ] b a ñ a + b π θ dθ + b a π ô θ θ dθ π π b a a + b π 6 (b a ) (a + b )π a b I F() () d F() () () d + () () + + d () d () + () () d () d () + d () ( + ) () d + () () + ( + )

8 R () () e () (e (+i) ) e e e () d d () d e (+i) d e e i + i i e e i 5 e () d e 5 (() + ()) u e () d e e (() + ()) ( ) d e u u e u u eu ( u + u) ( ) d (( ) + ( )) u + d + (u ) 3 u3 u 3 Ä ä ( ) 3 u e d u + u (e ) t t + t [ ] ] ], π t, π t > t t + t > + > t t t+ t t u π t S + C π S C π 4 t t+ t [, π ] S C t u I π u u + u u [, π ] u I π u u + u C π 4

9 I u t I J u t ], π[ > 4 u Å + u + u [( + u)] [( u)] 3 J J π u Å t t u u + ( [( u)] [(u + )] (( ) ( + )) ( ) ( ) ) K u t K π 4 π 4 t ( t) K 4 4 ( ï u K ( u ) Å (u ) u + (u + ) + u + ò ( + ) + ï [( u)] + u + ò ) + [( + u)] L u t L u + u Å K u + u (î ó (u + ) î ( + u ó ) ( + )

10 ï ò t t I () ( + t ) + + ( + ) ( + t ) + ( + ) + + ( + ) (I () I + ()) ( + )I + () ( + ) + + ( + )I () + I () N l + I () N l l N l π l π + ( ) N l k + l k + k ()! (!) [, ] ( ) e! ( ) e! I e (I ) I + ñ ( ) + ( + )! I I ñ ( ) ( ) + d e! ( + )! k ô e + I k I k+ ô ( ) e d I! k (k + )! k e ( + )! ( + )! k! I e d e e I + k k! k! k

11 t + t I I + I + t + t + + t S t + (I ) t + () k+ (I k + I k ) k () k+ I k S () + I () I I + () + I I I (I ) Q k () k I k k N p N C I,p I,+p t ( t) p p + I,p+ I,p ñ ( t)p+ t p + ô t ( t) p+ + p +! (p + ) (p + ) I,p+!p! (p + )! I,p+ t +p m + +!p! I,p ( + p + )! I 3 ï ò ( ) 3 t t t ( t ) 3 t ( t) t 3 [I I ] I + 3 I. C I ï ò 3 ( t) 3 3.

12 I () () ( + 3) (5) I +! (+4)! + (+)! () () ( + 3) (5) 3 +3!( + )! ( + 4)! [, ] [, ] C t u u I u ( u ) Å Ç u å() k u k k k Å Ç å() k u k+ k k () k u k+ k k () k k k + 3 k k +3!( + )! I ( + 4)! () k!( + )! + k k + 3 ( + 4)!. t /3 3 Ä /3 ( t + ) 3 ä t 5/ ( t + ) + (t) t 3/4 ( t 4 t + 3 ) + 5/ Ä (t ) ä C t u. ψ() + f(t) f R ψ R ψ () f( + ) f().

13 g : t t +e R G R R f() G( 3 )G( ) F t R f R f () 3 G ( 3 ) G ( ) 3 g( 3 ) g( ) e 3 + e R + (t ) (t ) (t ) R (t ) R (t ) (t ) ], + [ t [, ] < t () t () + () + t + R ï t t t t + R + t t + + () ò () t + t t + t t t t t + t t t t

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