Le 21/05/2012 10:07, Bernard Lempel a écrit :
> 2,7268 : fond cosmologique en Kelvin
> 2,7268 : Dimension fractale de l'éponge de Menger, nombre sans dimension
> 2,7252 : Borne supérieure de Tsirelson expérimentale, nombre sans dimension
>
> Tu comprendras éventuellement pourquoi je faisais l'hypothèse saugrenue,
> qu'il y aurait, peut-être, un lien entre le CMB et la théorie des quantas.
pour que cette coincidence ait un sens physique, il faudrait que l'unité
"1 Kelvin" ait un sens non-arbitraire.
Or 1 Kelvin, c'est juste 1/100 de la difference entre l'eau gelée et
l'ébullition sous 1 atmosphere terrestre.
par ailleurs si tu tappe 2,7268 dans ,'inverseur de Plouffe
http://pi.lacim.uqam.ca/fra/ ou
http://oldweb.cecm.sfu.ca/cgi-bin/isc/lookup?number=2.7268&lookup_type=simple
, tu trouves au moins 687 expressions mathematiques donnant ce resultat.
Dont certaines assez compactes. (elles le seraient bien plus en
autorisant les constantes non purement mathématiques).
2726793474027470 = (0191)
Prod(1-(7/6*n^3-9/2*n^2+55/3*n-3)/C(2*n,n),n=1..inf)
2726793604477093 = (0131) sum(1/(52*n^2-100*n+143),n=1..inf)
2726794058449347 = (0131) sum(1/(93/2*n^2-113/2*n+14),n=1..inf)
2726794119590419 = (0001) sr(3)/(2^(1/3)-Ei(1))
2726794145766232 = (0297) BesselK(1/2,26/19)
2726794355392294 = (0001) (ThueMorse-exp(-Pi))/GAM(2/3)
2726794442519990 = (0325) 4/(2^(3/4)-6^(3/4))^(1/2)
2726794553905225 = (0001) GAM(1/24)^(GAM(11/12)/BesK(0,1))
2726794645446290 = (0062)
sum((-1)^(n+1)/(5/3*n^3-3/2*n^2+11/6*n+13)/C(2*n,n),n=1..inf)
2726794658092567 = (0001) (sin(Pi/5)+exp(-Pi))/exp(Pi)
2726794765677685 = (0001) GAM(5/24)^TwinPrim*GAM(23/24)
2726794919243112 = (0325) 29-3^(1/2)
2726795078036276 = (0001) (TwinPrim*exp(gamma)+Golomb)/TwinPrim
2726795175356498 = (0314) cos(Pi*11/35)-cos(Pi*16/39)
2726795513364989 = (0404) Psi(16/21)+Psi(11/14)+Psi(17/18)
2726795565646152 = (0395) sum(1/C(2*n,n)/(3/2*n^3-17/2*n^2+30*n),n=1..inf)
2726795618797544 = (0325) 1/2*(26+14^(1/2))^(1/2)
2726795752698506 = (0008) sum((1/2*n^3+6*n^2-17/2*n+19)/n^n,n=1..inf)
2726795754503616 = (0002) sum(1/(5^n*(5/3*n^3+2*n^2-20/3*n+11)),n=1..inf)
2726795898287986 = (0001) (Zeta(3)-exp(1/E)*Zeta(1,2))/Zeta(1,2)
2726795936366283 = (0250) F(11/12;21/23;1)
2726796137756572 = (0001) ln(2+sr(3))^arctan(1/2)+BesI(1,2)
2726796276481704 = (0001) ln(1+sr(2))+exp(1/2)^GAM(3/4)
2726796613799093 = (0010) sum((10/3*n^3-13*n^2+56/3*n+9)/(n!+1),n=1..inf)
2726796784528217 = (0003) sum(1/(5^n+(16*n^2-4*n+50)),n=1..inf)
2726796917668546 = (0260) F(11/12;1/12,3/8,5/7,1/5;1)
2726796935557513 = (0264) sum(1/(-2*3^n+4^n-2*18^n-1),n=1..inf)
2726797101220613 = (0250) F(36/53;23/34;1)
2726797465829240 = (0259) F(8/11,4/11;1/9,6/7,1/6;1)
2726797791021540 = (0001) E*BesJ(1,1)*BesI(0,2)
2726797930951645 = (0001) K(1/sr(2))^Zeta(1,2)/(arctan(1/2)^Zeta(1,2))
2726797931801728 = (0325) 12^(1/3)-2^(1/4)+7^(1/4)
2726798015491317 = (0259) F(9/11,4/11;4/9,6/7,3/5;1)
2726798301302993 = (0001) GAM(1/4)^GAM(1/3)/(GAM(11/12)^GAM(1/3))
2726798458397010 = (0395) sum(1/C(2*n,n)/(7/2*n^3-41/2*n^2+46*n-5),n=1..inf)
2726798516838843 = (0001) (log(gamma)*ln(Pi)+GAM(5/12))/log(gamma)
2726798800620589 = (0002)
sum(1/(5^n*(11/3*n^3-43/2*n^2+305/6*n-25)),n=1..inf)
2726799498706690 = (0063) sum((n^3-7/2*n^2+45/2*n-14)/Fibo(n),n=1..inf)
2726799503613418 = (0006) 1/3667303
2726799568803477 = (0010) sum((1/3*n^3+13/2*n^2-29/6*n+6)/(n!+1),n=1..inf)
2726799601730598 = (0400) sum(1/(n!+1/2*n^3-n^2+11/2*n+1),n=1..inf)
2726799686151135 = (0325) 1/5*(10*5^(1/3)+10^(2/3))^(1/2)*5^(2/3)
2726799743769717 = (0325) 1/18*(18*6^(1/2)-20)^(1/2)
2726799819036091 = (0250) F(39/46;38/45;1)
2726800063982510 = (0001) ln(3)*Bernstein/GAM(5/6)
2726800264017965 = (0131) sum(1/(87/2*n^2-183/2*n+161),n=1..inf)
2726800341337942 = (0064)
sum((5/6*n^3+5/2*n^2-19/3*n+22)/(Fibo(n)+1),n=1..inf)
2726800365768639 = (0002) sum(1/(2^n*(7/3*n^3-3*n^2+11/3*n-1)),n=1..inf)
2726800481030620 = (0192) (-Golomb+1/3)/(-BesJ(1,1)+1/3)
2726800528591366 = (0131) sum(1/(75/2*n^2-5/2*n+48),n=1..inf)
2726800544117315 = (0001) (Zeta(3)*GAM(11/12)+ln(5))/GAM(11/12)
2726800723323469 = (0311) sin(Pi*8/53)*sin(Pi*11/54)
2726800779757879 = (0250) F(9/32;7/25;1)
2726800833125462 = (0001) 1/3*cos(Pi/12)+ZeroBesJ(0,x)
2726800981638076 = (0011) sum((2*n^3-13/2*n^2+39/2*n+3)/(n!+2),n=1..inf)
2726801162816587 = (0325) 11^(2/3)/(12^(1/4)-20)
2726801172379513 = (0001) Pi^Feig1/(gamma^Feig1)
2726801224019439 = (0001) Pi^exp(1/Pi)*BesI(1,1)
2726801262085281 = (0001) BesI(1,1)*W(1)^GAM(17/24)
2726801324310104 = (0005) Digits of gamma from rank 548
2726801662779442 = (0261) -5+4*x-5*x^3-x^4+x^5
2726801734245902 = (0399) 1/36673
2726801829038165 = (0250) F(17/26;28/43;1)
2726802021237707 = (0131) sum(1/(30*n^2-20*n+101),n=1..inf)
2726802438214016 = (0002) sum(1/(3^n*(7/6*n^3-2*n^2+59/6*n+6)),n=1..inf)
2726802464244597 = (0010) sum((5/6*n^3-5*n^2+127/6*n)/(n!+1),n=1..inf)
2726802465496473 = (0131) sum(1/(83/2*n^2-133/2*n+128),n=1..inf)
2726802494044780 = (0001) (cos(1)+GAM(23/24))^sr(5)
2726802624552579 = (0003) sum(1/(5^n+(23*n^2-20*n+57)),n=1..inf)
2726802782102415 = (0005) Digits of E from rank 35483
2726803249970201 = (0001) (2/3)^W(1)+GAM(11/24)
2726803250647480 = (0198) Im((-10+20*I)^(16/13))
2726803387812287 = (0263) 4+14*x+9*x^3
2726803609730969 = (0001) sin(Pi/12)/(Zeta(1,2)^cos(Pi/5))
2726803838739739 = (0001) GAM(5/12)/(sr(5)+GAM(1/6))
2726804116367141 = (0001) exp(gamma)+cos(Pi/12)^ln(5)
2726804316089315 = (0198) Im((-4-4*I)^(41/21))
2726804337439112 = (0008) sum((4*n^3-29/2*n^2+79/2*n-15)/n^n,n=1..inf)
2726804544925286 = (0001) NineConst^Bernstein*Zeta(1/2)
2726804962145512 = (0001) TwinPrim/(Parking+GAM(1/24))
2726805112073204 = (0001) (GAM(1/3)-exp(sr(2))*GAM(11/24))/GAM(11/24)
2726805474048208 = (0003) sum(1/(3^n+(7/3*n^3-2*n^2-4/3*n+3)),n=1..inf)
2726805500664056 = (0001) (Li4(1/2)-sin(Pi/5))/GAM(13/24)
2726805805580233 = (0250) F(22/29;34/45;1)
2726806448894023 = (0404) Psi(1/24)+Psi(5/21)-Psi(9/16)
2726806647085473 = (0131) sum(1/(44*n^2-47*n+7),n=1..inf)
2726806918402484 = (0062) sum((-1)^(n+1)/(7*n^2-21*n+27)/C(2*n,n),n=1..inf)
2726807380662090 = (0325) 1/3*(3^(1/4)*9^(3/4)+11^(3/4))^(1/2)*3^(3/4)
2726807413962308 = (0395)
sum(1/C(2*n,n)/(11/3*n^3-14*n^2+67/3*n-10),n=1..inf)
2726807749689016 = (0260) F(11/12;1/10,5/8,1/7,1/2;1)
2726807847417367 = (0001) exp(-Pi)/(ln(Pi)+BesJ(1,1))
2726808048312491 = (0260) F(4/9;2/9,5/7,1/6,3/4;1)
2726808143341995 = (0001) BesI(0,2)^Backhouse-Lehmer
2726808271914459 = (0002) sum(1/(3^n*(5/3*n^3-8*n^2+43/3*n+9)),n=1..inf)
2726808666698577 = (0001) GAM(23/24)*(Zeta(3)+Backhouse)
2726808937673199 = (0192) (cos(Pi/12)+2)/(BesK(0,1)+2/3)
2726808966462802 = (0001) sin(1)^Feig2/(sr(2)^Feig2)
2726809237158227 = (0002) sum(1/(5^n*(3/2*n^3+3*n^2-17/2*n+12)),n=1..inf)
2726809430985985 = (0011)
sum((11/3*n^3-33/2*n^2+281/6*n-25)/(n!+2),n=1..inf)
2726809449452251 = (0325) 11^(2/3)-12^(1/3)*3^(3/4)
--
Fabrice