Mathematische Konstanten nahe Physikalischer Konstanten (Mathematical constants near Physical Constants) |
1. Verhältnis der Magnetischen Momente: Elektron/Neutron µe/µn = 960.920 50(23)
siehe CODATA http://physics.nist.gov electron-neutron magnetic moment ratio
A=-254843 i=-2 NK=9609205067716064247, 96/π+278π+57 =960.9205067716064247...
A=-254842 i=-2 NK=9609205055805815326, (85e^π+24π-113ln(π)+7atan(π))/2 =960.9205055805815326...
A=-254841 i=-2 NK=9609205050969917902, (3089π)/10-299/(10π) =960.9205050969917902...
A=-254840 i=-2 NK=96092050403490252087, (451/(3ln2)-(497ln2)/15+802/(15ln3)+(1108ln3)/15-268/15)*π=960.92050403490252087...
A=-254839 i=-2 NK=96092050403490252085, 102*π+2*π*sqrt(10391)*cos(atan(sqrt(797526883)/2118251)/3)=960.92050403490252085...
A=-254844 i=-2 NK=9609205028244135322, (303+sqrt(95321))/2 =960.9205028244135322...
A=-254845 i=-2 NK=9609204968974873095, A133731*832-π =960.9204968974873095...
A=- 31281 i= 5 NK=9609205228104979473, (A-31281*10^4-39279)*10³ =960.9205228104979473...
2. Quotient der Ruhmassen: Proton/Elektron mp/me = 1836.152 672 47(80)
siehe CODATA http://physics.nist.gov proton-electron mass ratio
...............NK=1836152679966861539847752863023830342491... (30*Pi^5+1/cosh(Pi)+1/sinh(Pi))/5 https://vixra.org/pdf/1410.0054v6.pdf
A=-254851 i=-3 NK=1836152672470517964420305082780625612339... agm(1000,2360*pi-22021/5-1257/(5*pi))
A=-254850 i=-3 NK=1836152672470208157555945885035426091099... agm(67/(7 e)+(15574*e)/7-4372,2000)
A=-254848 i=-3 NK=1836152672469999999999493282280631397074... sqrt((2247+((5*(A093525*1111-8))/(3*(A093525*2334-11))))*1500)
A=-254849 i=-3 NK=1836152672469999998995088237542599144706... sqrt((2247+(13145672*pi)/64755539)*15)*10
A=-254847 i=-3 NK=1836152672469999627738634865622501655601... 1/sqrt(1-sqrt(A-254852))
A=-254846 i=-3 NK=1836152672469997970813974129734430239158... 2917/4+209/(pi*2)+(1367 pi)/4
3. Quotient der Ruhmassen: Neutron/Proton mn/mp =1.001 378 419 18(46)
siehe CODATA http://physics.nist.gov neutron-proton mass ratio
A=-320661 i=0 NK=1001378418637738077993199436788138632792 agm(1Y39/1Y37,M88/M87)
A-1709777 i=0 NK=1001378418739784685917882377015166101397 agm(1001,5690981/5681)/1000
A-1709778 i=0 NK=1001378418802644653556823701387579764880 agm(...
A=-254853 i=0 NK=1001378418805489407307326126612499319631 hypergeom2F3([1/1K,1],[ZY/1Z,ZY/1Z,14/Y],1/M)
A-1709779 i=0 NK=1001378418839047004579773280700950753493 agm(1001,.../1773)/1000
A=-?????? i=0 NK=1001378418926740104417443128686512901669 BesselJ(0 , (5 pi!)/6-21/(8 pi)-(13 pi)/12)*e
A=-254861 i=0 NK=1001378418999999999311413434337530580444 [Z18Z48MY/38448Z9M*exp(Z18Z48MY/38448Z9M)
A=-254860 i=0 NK=1001378419000000000004346366099831802065 [x*exp(x),x=(YM9+8MM*e-19*e²)/(Z*(-Z41+849*e+YZ*e²))]
A=-320659 i=0 NK=1001378419006130264551446943396925460139 agm(1KK13/1KKKK,8Z49/8Z37)
A=-320671 i=0 NK=1001378419030421154409506283726863560316 x=x-tanh(x)*x+3ZKM3/4ZK1K
A=-?????? i=0 NK=10013784191005816 agm(Ziegenfaktor A133731...
A-1709762 i=0 NK=1001378419103999979263861701263282827623 1/tanh(log(1/4(4e²+31pi+10pi²-ZZ-17sqrt(Z)-10e)))
A=-254868 i=0 NK=1001378419116141114453866068596247775684 34K/(3Y1-[A117233]*9)
A=-320677 i=0 NK=1001378419116866044991203852182520709811 x=cos(x)+33465/7Z398
A=-320673 i=0 NK=1001378419121679581584919170263470274179 x=LambertW(x)^x+Z4K34/YY3YY
A=-?????? i=0 NK=10013784191255654 mögl. Anzahl Quarks...
A-1709796 i=0 NK=1001378419130864148845778693673366155052 (11/15 + 46/(15*(3*[A115365]-2))^3
A=-320679 i=0 NK=1001378419131856251245835241992253399319 x=log(x)+(1991*A117240)/80Y+1
A=-320672 i=0 NK=1001378419149234397086174937008562076495 x=LambertW(x)^Z+13ZMM8/19Y341
A-1709757 i=0 NK=1001378419155912601570938190468693025187 tanh(73/7)*( Z9/(138-9Z*A062073)-7/46)
A=-?????? i=0 NK=10013784191605206 exp-Iteration...
A=-254870 i=0 NK=1001378419163181965744864426516102087904 (13K1*pi)/14-(1K711*[A081760])/ZK
A=-254869 i=0 NK=1001378419163182706494468386350431406378 (479K*sqrt(Z))/4413-78Y/1471
A=-320668 i=0 NK=1001378419169821414532796808836471477501 agm(18/17,M3349/MM998)
A=-?????? i=0 NK=10013784191725217 exp-Iteration...
A=-845746 i=0 NK=1001378419174405376232537346528313897922 sum{3,1,-1-3-1,1/[n!-1YY4M8/77YZ3]}
A-1709775 i=0 NK=1001378419177161529790855854075954883887 1/erf(2/5 *pi*csch(577/837)^2)
A=-254864 i=0 NK=1001378419178365178627184012172570900433 (A-47674*x+A-167317)/(x+1);x=ZYMK1/1K^4
A-1709767 i=0 NK=1001378419178927826143867815141898195645 1/erf(556Z/(77(80-77[Sierpinski's constant A062089]))-160/77)
A-1709766 i=0 NK=1001378419179122086500708038203545601224 (x²+1)/(x²-1),x=717 (A039662)/7+Z7
A-1709765 i=0 NK=1001378419179385912701155425920789833209 (Z^x+1)/(Z^x-1),x=41/40-159/(40 e)+(161 e)/40
A-1709774 i=0 NK=1001378419179404529596048627062804053423 1/erf((3301[Hard Hexagon Entropy Constant A085851]-Z6*pi)/Z000)
A-1709754 i=0 NK=1001378419179524060562899261020361490684 (Z^x+1)/(Z^x-1),x=1/30 (7 e^pi+Z pi+136 log(pi)-7 atan(pi))
A-1709768 i=0 NK=1001378419179695410086669469297596833554 1/erf(Z0/(105 (Gelfond-Schneider Constant A007507 )-Z71))
A=-?????? i=0 NK=10013784191798965 exp-Iteration...
A-1709756 i=0 NK=1001378419179964486423481656305287167670 tanh(647/6Z)*( Z9/(138-9Z*A062073)-7/46)
A-1709769 i=0 NK=1001378419179983503023134151353470008844 zeta(1595/107-10/(107*[A093525]))
A=-320666 i=0 NK=1001378419179999325889068136365768501476 agm(sqrt(3),Z13Y993/4Y1MK4Y)
A=-320669 i=0 NK=1001378419179999539338603481206318307679 log(133MY31/491KKY)
A-1709752 i=0 NK=1001378419179999717641854396361557304111 (Z^x+1)/(Z^x-1),x=41/70+5157/(70 (3+5 [A030171]))
A=-320670 i=0 NK=1001378419179999957537347744211801825899 x=exp(-Z*x)*(x+1)+1K9Y4Y33/1498KZ1K
A=-254859 i=0 NK=1001378419179999995004381483384752774022 [x*exp(x);x=tan(cot(7Z81KZY1/1111Y989))]
A=-254857 i=0 NK=1001378419179999997985309169669823714987 agm(1,ln(cot(18894M1/34733MM))+1/Z)
A=-320680 i=0 NK=1001378419179999998136241946126483210385 x=1/Sqrt(Z-x^Z)-90Z3Z9/(753743*1K^Y*pi)
A=-254855 i=0 NK=1001378419179999999983693666049343226246 (3/Z-x)^x ;x=(441*e²-Y3Z-14KY*e)/(3*(e-4Z9)*(e-1))
A=-254862 i=0 NK=1001378419179999999992196793776990238829 1/(1-(1K*pi*cos(Z984KKY8/1913M449)^Z)/3)
A-1709759 i=0 NK=1001378419179999999999238139570581891795 1+(Z4*pi)/(6011-4393pi-599pi²+30Z9*pi*pi!)
A=-254856 i=0 NK=1001378419179999999999924226161478778492 (3/Z-x)^x ;x=(Z*(389*pi-ZY-119*pi^Z))/(3*(ZMZ-1K3*pi+4Y3*pi^Z))
A=-254858 i=0 NK=1001378419180000000003588430722272444803 agm(1,9K4777Z38Z/9KZZ8891M9)
A=-254863 i=0 NK=1001378419180000000020603148067727329653 A133731/Z+1Y7YK3/(YKZ8Y3*pi)+7937*pi/773MZ
A-1709755 i=0 NK=1001378419180000023162084133431400984361 tanh(49099/4705)*( Z9/(138-9Z*A062073)-7/46)
A=-?????? i=0 NK=1001378419180005284573401179114948104835 (Z^x+1)/(Z^x-1),x=Z94/(Z3 [Gauss constant A014549])-33Z/69
A=-?????? i=0 NK=1001378419180029826851612267108619787313 (exp(x)+1)/(exp(x)-1),x=15699/(8000*A105415-4040)+159/40
A=-320658 i=0 NK=1001378419180061792314142448182330855794 agm(1KK1/1KKK,78M8Y/78Y47)
????????? i=0 NK=1001378419180145551987770032480320195093 (e²)!/(1407/(200 (Plouffe's B constant A086202)-95)-506/5)
A=-?????? i=0 NK=1001378419180394282044080099 (Z^x+1)/(Z^x-1),x=ZZZ/(Z53 pi)+(179 pi)/55
A=-?????? i=0 NK=10013784191827128 mögl. Anzahl Quarks...
A-1669990 i=0 NK=1001378419185947381272084372797006960502 ([A-1669809]*x+[A-1669628])/(x+1);x=1M37/ZMK
A=-320681 i=0 NK=1001378419194692403403204495882643255986 x=1/Sqrt(Z-x^Z)-log(787Z8Z/787Z79)
A=-254854 i=0 NK=1001378419197330406061948818940376796179 hypergeom2F3([1/7,1],[Z4/13,Z4/13,YK8483/ZKKKKK],1/1Z)
????????? i=0 NK=1001378419199072749495090642348749492661 (Z^x+1)/(Z^x-1),x=16 - 84/(9 + Z*Pi)
A=-254874 i=0 NK=1001378419201804026058391337992341212095 Z/(Y*log(Z))+(Z7*log(Z))/ZY-1/(ZY*ln3)-(Z*ln3)/ZY-(log(Z43))/(ZY*ln3)
A=-254872 i=0 NK=1001378419217873089484253662340510610621 log(7/Y+sqrt(Z)-(17*e)/1K-(17 pi)/1K+pi^Z)
A=-320682 i=0 NK=1001378419219452780113621446831800361683 sum{1/(n!+n-20651/80019)},n=1...inf
A=-?????? i=0 NK=1001378419221139952346370082394575400253 ([A-320661]+[A-254871])/2
A=-320663 i=0 NK=1001378419223767264469533915348434617454 1/agm(733/73Z,Z3Z31/Z33Z7)
A=-254865 i=0 NK=1001378419238102220020839473526169938343 pi*31/18Y+A094692
A=-?????? i=0 NK=1001378419244000000000798803160127945689 (1+(509-16sqrt(2)+113e+42e²+711pi-315pi²)²/36)/((509-16sqrt(2)+113e+42e²+711pi-315pi²)²/36-1)
A=-?????? i=0 NK=1001378419255000000000200683511243387813 (1+(7+959e+435e²+295pi+358pi²)²/72900)/((7+959e+435e²+295pi+358pi²)²/72900-1)
A=-320667 i=0 NK=1001378419269440555797843894064490990090 agm(14/13,3Z713/3YZZ9)
A=-?????? i=0 NK=1001378419273994738029380681367657204841 FresnelS((700[plouffe's B constant A086202]-943)/(307(plouffe's B constant)-720))*2
A=-?????? i=0 NK=1001378419273999999998496896763366572532 pi/(Z atan(4/99 (317 e^pi+994 pi+754 log(pi)+99 atan(pi))))
A=-?????? i=0 NK=1001378419284000008348802341813385323110 FresnelS((269-131[A117238])/(601[8th Hundred-Dollar Challenge constant A117238]-54))*2
A=-?????? i=0 NK=1001378419295810190310307075444474347484 3/2-71/(81*(nested radical constant A072449))
A=-?????? i=0 NK=1001378419304000000034747304347063250453 A133731+421/7888+751/2958/pi-183*pi/1972
A=-?????? i=0 NK=100137841931397598844044729916236882053? tanh((371*(Masser-Gramain constant)-3)*2/(303*(A086058)+200))/A173571
A=-320685 i=0 NK=1001378419328934341378501534494911635204 318Y7/2114Y=sum{1/(n!+n-A-320685)},n=1...inf Beispiel 93
A=-320675 i=0 NK=1001378419339998817344305919751796975850 atan(498347/(ZY1 (YKZ*A093540+34Y))+3Y/YKZ)
A=-320674 i=0 NK=1001378419340008487201401262829061142816 atan(19KK/9K1-319M9Y/(9K1 (9K1*A12245+YYK)))
A=-?????? i=0 NK=1001378419341400540795683758476908406490 Ei((10+188 pi+35 pi^2)/(161+129 pi+84 pi^2))
A=-?????? i=0 NK=1001378419343955414711535293261331303862 BesselJ(-1/2 , 191/(107 (107*(6th hundred-dollar challenge constant)-2))+80/749)
A=-460493 i=0 NK=1001378419391220521053937505520412182190 log(37*e^Z+9*pi-Z6*pi^Z-7-13*e)
A=-460491 i=0 NK=1001378419400868623764700252195508623679 (A086058*7Y-8)/((A086058*38-Y)*Z)
A=-460495 i=0 NK=1001378419439862094472114405064636222472 agm(tanh(x),1/tanh(x)),x=log(Z3Y3Z7/4Y33Z)
A=-460492 i=0 NK=1001378419441111111996296364012467050272 (19M-4YY*pi+3Y*pi^Z)/(9Z*pi^Z-1Y8-YZ1*pi)
A=-?????? i=0 NK=1001378419448489683061037631061484839274 41*pi/250-[mean cube-in-tetrahedron volume A093524]
A=-320660 i=0 NK=1001378419579767576695242612969793810373 agm(77K/7M9,3438/3433)
A=-320665 i=0 NK=1001378419616018023355500822256181123175 agm(1/3,77Y7/Z3ZK7)*3
A=-254867 i=0 NK=1001378419629990629745081746866904507591 (Z888/7-ZZ9*A130834)*cot(9Y/8Z)
A=-254866 i=0 NK=1001378419629999634017602542577690133185 (11Z8934 pi^Z)*cot(9Y/8Z)/48MY97Y
A=-?????? i=0 NK=10013784196441189442858584278251958 ((34 [Chaitin's Constant A100264])/583+1)^3
A=-254871 i=0 NK=1001378419804541826699540728001012167714 3Y1/(Z*A079586+81)-3
Die Ziffern 0, 2, 5, 6 sind zum Knobeln in den Buchstaben K, M, Y, Z versteckt.
4. Feinstrukturkonstante
bis 2016: 0.007 297 352 5698(24)
ab 2016: 0.007 297 352 5664(17) {auch 7.297 352 5664(17) *10^-3 }
ab 2019: 0.007 297 352 5693(11) {auch 7.297 352 5693(11) *10^-3 } siehe CODATA fine-structure constant
ab 2020: 0.007 297 352 56279(59) siehe nature: Determination of the fine-structure constant with an accuracy of 81 parts per trillion
----------------- 2019 nicht im Toleranzbereich... ab 2020 doch wieder! -------------------------------------------------
A=-?????? i=0 NK=0.007297352562204556976241508076529937139957 (126Pi-11*Pi*Pi!-47-10*Pi²)/(76Pi)
A=-?????? i=0 NK=0.007297352562313280898575367852269157077550 86613/11869099
A=-?????? i=0 NK=0.007297352562479534373585706561980573094362 HypergeometricPFQ[{9/11,7/9},{4/9,6/7,2/7},22219141/22219142]/10-1
A=-?????? i=0 NK=0.007297352563068799145079989761574031576983 (794-63*Pi²)/(7512*Pi)
A=-?????? i=0 NK=0.007297352563372418398151662395363248376621 124225/17023297
----------------- ab 2020 nicht mehr im Toleranzbereich -------------------------------------------------
A=-?????? i=0 NK=0.007297352564690055514868687836131094463897 53029/7266882
A=-?????? i=0 NK=0.007297352564725646605651320044337274587826 Pi/34350904230^(1/4)
A=-?????? i=0 NK=0.007297352564901312508538550938388033123505 (2^(2/3)*(a)^(1/3)-440-31340*(2/(a))^(1/3))*Pi/298,a=21056803+149*sqrt(20664833009)
A=-?????? i=0 NK=0.007297352565087052846028593077688693693961 43001/5892685
A=-?????? i=0 NK=0.007297352565350923945388368762528064055306 (142-1411/(a)^(1/3)+(a)^(1/3))*Pi/150,a=50*sqrt(1185773339)-1720937
A=-?????? i=0 NK=0.007297352565873081806743840327906904957766 3/(430-269*log(2)/Pi²)
A=-?????? i=0 NK=0.007297352566071001280264678721804796320616 32723/4484229
A=-?????? i=0 NK=0.007297352566197941133067001334411260228126 51279/7027069
A=-?????? i=0 NK=0.007297352566216512312308628501487515169105 55918/7662779
A=-?????? i=0 NK=0.007297352566399908589860712659303866763265 524457/71869489
A=-?????? i=0 NK=0.007297352566400835603445947468394210806760 547652/75048039
A=-?????? i=0 NK=0.007297352566401426636030731685749859235880 sinh(4954/93877)²*Pi*5/6
A=-?????? i=0 NK=0.007297352566409959592287445205294790429287 969801/132897649
A=-?????? i=0 NK=0.007297352566410993105375648378725003347770 1062581/145611849
A=-?????? i=0 NK=0.007297352566425130850983363746285826528964 Pi/34350904198^(1/4)=Pi/(2^35-8834170)^(1/4)
A=-?????? i=0 NK=0.007297352566438883556547420173152345897321 hyg2F3(9/11,7/9,4/9,6/7,2/7,22220665/22220666)/10-1
A=-?????? i=0 NK=0.007297352566444302295534165878793240165467 510040/69893841
A=-?????? i=0 NK=0.007297352566454927229256957036805718699954 ((log(8)+9+6Pi-35 log(3))*Pi+29-2 Catalan)/54
A=-?????? i=0 NK=0.007297352566460492254825265716142416624993 296646/40651181
A=-?????? i=0 NK=0.007297352566470366413930104133606155145632 236339/32386951
A=-?????? i=0 NK=0.007297352566480787709660411794824042891878 194588/26665561
A=-?????? i=0 NK=0.007297352566490634384449270525122398939123 166754/22851301
A=-?????? i=0 NK=0.007297352566503828982687724424457254246686 hyg2F3(9/11,7/9,4/9,6/7,2/7,22220690/22220691)/10-1
A=-?????? i=0 NK=0.007297352566631121594008644786907413983404 hyg2F3(9/11,7/9,4/9,6/7,2/7,22220739/22220740)/10-1
A=-?????? i=0 NK=0.007297352566633302448196239073813547626849 hyg2F3(9/11,7/9,4/9,6/7,2/7,999999954997/1e12)/10-1
A=-?????? i=0 NK=0.007297352566752195516567874319386704551804 agm(32723/4484229,22695/3110032)
A=-?????? i=0 NK=0.007297352566761011435024761437276303208733 hyg2F3(9/11,7/9,4/9,6/7,2/7,22220789/22220790)/10-1
A=-?????? i=0 NK=0.007297352567433389752902864021977908908975 22695/3110032
A=-?????? i=0 NK=0.007297352567539866968965176666009321685166 3e-8sqrt(1+e)-10Pi+2Pi²+21sqrt(1+Pi)-6sqrt(1+Pi²)-4
A=-?????? i=0 NK=0.007297352568076759539149668040064617314322 (4e^(3e-13/Pi+6*Pi-3-4/e)*Pi^(4-9 e)*sin(e*Pi)²*sin(2e*Pi)²)/(cos(2e*Pi)-1)^4
A=-?????? i=0 NK=0.007297352568098809630493607291131594475047 116364/15946057
A=-?????? i=0 NK=0.007297352568105130816982943065334500693443 log(38449/38062)/(log(4)
A=-?????? i=0 NK=0.007297352568653853422694733690852932089174 www.chip-architect.com/news/2004_10_04_The_Electro_Magnetic_coupling_constant.html
A=-?????? i=0 NK=0.007297352569693032062830908304083517935 832/(9*(A085848=second Foias constant)+666)-11/9
A=-?????? i=0 NK=0.007297352569738292969351203540308111378 17306/2371545
A=-?????? i=0 NK=0.007297352569738292969361815915039381169423 (9x^5+71x^4+533x³+180x²-3014x+7=0)*Pi
A=-?????? i=0 NK=0.007297352569802870342054069747172735598 1-tanh((485+A086201)/(190-107*A086201))
A=-?????? i=0 NK=0.007297352569819786655486913613052859882 (37-16*A118428)/(25*A118428+653)
----------------- alte Obergrenze 2019 -------------------------------------------------
A=-?????? i=0 NK=0.007297352570631861148425381809388844813 (260x³-211x²+431x-1=0)*Pi
A=-?????? i=0 NK=0.007297352595142889257584331238777231787 135/8 -55*(A062073=Fibonacci constant)/4
Alle mathematischen Konstanten sind in meiner Datenbank für mathematische Konstanten http://pi.gerdlamprecht.de zu finden. Bis auf wenige Ausnahmen immer mit einer Genauigkeit von mindestens 1020 Dezimalstellen.