From the study bench of
Marvin Ray Burns
(317) 371-6571
Last update 3/29/2008 6:55= :31 PM
=
This is
the 2nd link.
=
Intro to
MRB was started at
http://=
www.mapleprimes.com/blog/marvinrayburns/mrbconstant
(Key decimal expansions begin on page 82.)
![3D"Q&A"](3D"QA-1_files/image001.gif")
<=
![endif]>
Q.
What is the MRB Constant and who ca= res?
A.
Late in 1998, a constructi= on worker named Marvin Ray Burns had a dream
that the all of the intege= rs wanted to get together and make themselves bigger.
They lined themselves toge= ther but the more integers that joined the stack -
the flatter the stack beca= me. Mr. Burns asked one of them,
"Why were you so unsu=
ccessful
at
"We are all roots.&qu= ot;
Marvin Ray Burns woke up, = started playing with his calculator, and a few months later named the MRB Constant.=
Simply put:
First consider 1.
Second consider the square= root of two.
Third consider the cube ro= ot of three.
Now we also want the fourt= h root of four, fifth root of five, and so on.
Now after we get all of th= ese we want to add them as an alternating series.
1^(1/1)-2^(1/2)+3^(1/3)- 4^(1/4)+5^(1/5)...
The sequences of partial s= ums have two limit points, which vary by one, since lim(= n^(1/n)) =3D 1 as n approaches infinity. Therefore, it
suffices us, in the crunch= ing out of digits of the MRB Constant, to focus on the sequence that ends in an even number being taken to its own root.
Straight forward crunching= out of digits of the MRB Constant is a great stress test for computers.
approx. 0.187859642462067120248517934054.
Nonetheless, here is a neat approximation!
4124*Pi/68966 =3D 0.1878596424818650830180080229.
Below we will see many such approximations.
Q.
What did Mr. Burns do on h= is calculator, in the process of defining the MRB Constant?
A.
Take the grand tour by goi= ng to the following URL:
![3D"Text](3D"QA-1_files/image002.gif")
Something unique was born = in Mr. Burns' imagination; he could not get rid of the idea
that the integers were try= ing to tell him something.
Daily he plays with intege= rs; he expects to find some new universal laws concerning them.
Q.
What practical application= could there be for the MRB?
A.
The partial sums of the se= ries (-1)^n*n^(1/n) can be used as signposts, of infinite precision and represent infinite dimension.
They can represent irratio= nal values of probabilities in a crucial range, approximately 0.19, 0.29, the transition from the second to the first quartile.
When computing the partial= sums of the MRB, we start with the value of 1-sqrt(2)/2 =3D 0.29289… or appro= x. 29%.
After an infinite number o= f terms, we end up at the value of the MRB=3D 0.1878… or approx. 19%.
Both series’ can be = used in this manor. The percentages are the same for an odd number of terms as they= are for an even number of terms.
However useful, we can rep= resent probability values with this alternating series.
Actually, the MRB Constant= is produced through stacking the sides of progressively larger n-dimensional c= ubes or hypercubes (here called cubes).
Cube one is of one dimensi= on with length of one unit in size.
On the right side of cube = one we place cube two taking up the right most points of cube one and thus linearl= y extends to the left of cube one by a specific value, i.e. 1-2^(1/2). Cube two is of= two dimensions and is of two units in size. On the top left of cube two we place cube three.
Cube three is of three dim= ensions and is of three units in size.
Linearly cube three extend= s to the right of cube one by a specific value, i.e. 1-2^(1/2)+3^(1/3).
![](3D"QA-1_files/image003.gif"=)
![](3D"QA-1_files/image004.gif")
Continue staking the cubes= in this manor. The specific value, i.e. MRB Constant represents the position of the infinite or last possible cube.
Linearly, we have the foll= owing graph of the stacking that looks like a ladder with smaller and smaller run= gs, as it goes up. It only goes up for the sake of viewing; actually, it is lin= ear and has no height. The base rung of the stack has length, 2^(1/2). The top = rung has length 1. Since we started the stacking on the left side, the left side= of the top rung represents the value, the MRB Constant.
Q.
What approximations involv= ing the MRB Constant are known to exist?
A.
Glossary:
(~) Means, "approxima= tely equal to."
(^) Means, "raised to= the power of." 2^3 Would mean 2*2*2.
(_) Is a space holder and = has no other meaning.
integral(f(x),x=3D a .. b)= Means, "the area under the Univariant graph of f = from x=3Da to x=3Db "
c^[n]d Means "raised = to the power of n times." (This is called a power tower.) 2^[5]3 Would mean 2^(3^(3^(3^(3^(3))))).
Ex Means, "*10^x"= ;
Log[y](x) means Log base y= of x.
[f digits] Means, "f = digits are omitted from the list."
Let m be the MRB constant = =3D limit(sum((-1)^x*x^(1/x),x=3D1..2*n),n=3Dinfinity)
~0.18785964246206712024851793405427= 32300559030949001387861720046840894772315646...
List:
The following list of 1067 approximations brings a great deal of order to the alternating sum of integ= ers, to rational powers, that is the MRB Constant:
I. &n=
bsp; =
;
(10317/10000-m)*=
Pi*20656~
54759.1111111117917
II. (27747/10000-m)*Pi*22509~182926.111=
111111448
III. (77/5000-m)*Pi*57396~-31097.0348971111111=
114233
IV. (20003/10000-m)*Pi*54587~ 310815.61111111=
11774
V. (1541/2500-m)*Pi*29079~39149.035571=
11111111586
VI. (10317/10000-m)*Pi*3227.5~8556.1111111112=
17458495849
VII. &=
nbsp; (11001/5000-m)*Pi*668.64~4227.11111111157839106849=
VIII. &=
nbsp; (6637/10000-m)*Pi*30013~44866.33080111111111581811
IX. (1387/2500-m)*Pi*60178~
69371.82222222224994188159
X. (5931/2000-m)*Pi*61453~536252.06222=
22222235033972793939
XI. (137/1250-m)*Pi*-67517~16599.724072222222=
225431660362098544866664
XII. &=
nbsp; (1387/2500-m)*Pi*30089~
34685.91111111112497094
XIII. &=
nbsp; (3067/2500-m)*Pi*21786~
71107.92222222225589747
XIV. &=
nbsp; (7621/10000-m)*Pi*55524~ 100166.92222222227591834
XV. &=
nbsp; (2451/10000-m)*Pi*5990800~1077300.9222222222657316=
4
XVI. &=
nbsp; (5679/2500-m)*Pi*292.72~
1916.2222222225292227429656
XVII. =
(1049/10000-m)*Pi*-3185.5~30.2222222225536275
XVIII. (3887/2500-m)*Pi*529.07~
2272.0222222222078855545
XIX. &=
nbsp; (10317/10000-m)*Pi*645.5~1711.222222222243491699
XX. &=
nbsp; (41/40-m)*Pi*53620~141018.133333333365549126204
XXI. &=
nbsp; (1591/10000-m)*Pi*-53245~4810.7433333333356470215
XXII. =
(929/5000-m)*Pi*-24664~159.589833333333326538631592
XXIII. (28631/10000-m)*Pi*65054~
546747.3483333333330642325
XXIV. (28599/10000-m)*Pi*651.3~5467.3133333333369845177
XXV. =
(11541/5000-m)*Pi*31793~211780.98423333333333783161
XXVI. (16687/10000-m)*Pi*34310~159616.8855333333333019
XXVII. (3977=
/2500-m)*Pi*514930~2269537.0444444444313996143767
XXVIII. (29633/10000-m)*P=
i*51685E4~4506571775.04444444440
XXIX. (13371/5000-m)*Pi*56131~438443.091674444444441129688
XXX. =
(28599/10000-m)*Pi*54275~455609.4444444447487098
XXXI. (407/5000-m)*Pi*-61927~20711.66044444444485108863049
XXXII. (907/=
2000-m)*Pi*22395~18689.384355555555508883688082
XXXIII. (20413/1000=
0-m)*Pi*53741~312920.655555555548997716
XXXIV. (3061/5000-m)*Pi*=
52816~70409.24990555555555174219889
XXXV. (6669=
/2500-m)*Pi*59761~465558.1555555555719604270334
XXXVI. (21951/10000-m)*P=
i*55178~347948.69168555555555
XXXVII. (5809/2000-m)*Pi*554.28=
~ 4730.545555555555
XXXVIII. (2343/2500-m)*Pi*55238/9~
14448.5555555551188242448
XXXIX. (19817/1000=
0-m)*Pi*66834~376644.05555555551354772180893999
XL. &=
nbsp; (41/40-m)*Pi*26.81~70.5090666666666827745631024262=
0033
XLI. &=
nbsp; (41/40-m)*Pi*26.81*2500~176272.66666666670693640775
XLII. =
(28599/10000-m)*Pi*325.65~2733.65666666666849225885499
XLIII. (11541/5000-m)*Pi*63586~423561.9684666666666756632203311
XLIV. (28599/10000-m)*Pi*21710~
182243.777777777899
XLV. =
(5809/2000-m)*Pi*277.14~2365.272777777777364
XLVI. (3383/1250-m)*Pi*50824~402131.07002777777777
XLVII. (1100=
1/5000-m)*Pi*167.16~1056.77777777789
XLVIII. (7383/2500-m)*Pi*=
634360~5511048.7777777777
XLIX. (7383/2500-m)*Pi*634360*0.5~2755524.388888888838
L. (27609/10000-m)*Pi*62914~508561.838=
8888888839
LI. (13791/5000-m)*Pi*55828/9~50089.888888888=
619398008
LII. &= nbsp; (9277/10000-m)*Pi*7000.81~16271.82188888888864668<= o:p>
LIII. &=
nbsp; (88813/50000-m)*Pi*70046~349537.027511173188888888828
LIV. &=
nbsp; (37717/25000-m)*Pi*70.1025~290.88888888873
LV. &= nbsp; (23383/25000-m)*Pi*70165~164762.57340108888888888<= o:p>
LVI. &=
nbsp; (39519/25000-m)*Pi*702342~3073396.288888888882
LVII. =
(87547/50000-m)*Pi*703224~3453224.888888888
LVIII. (5797/5000-m)*Pi*703564~
2147406.81888888888
LIX. &=
nbsp; (3147/2000-m)*Pi*7053.54~
30704.8888888887
LX. &=
nbsp; (46613/25000-m)*Pi*70.6022~371.8888888880
LXI. &=
nbsp; (86201/50000-m)*Pi*706628~3410179.728126807888888888
LXII. =
(20851/12500-m)*Pi*7.07250~32.88888888811
LXIII. (12499/10000-m)*Pi*707288~2359865.12831262888888888689 LXIV. (21687/12500-m)*Pi*707410~3438266.6433865888888888 LXV. =
(6483/6250-m)*Pi*.707838~1.888888888 LXVI. (50673/50000-m)*Pi*708829~1838489.7900888888888785 LXVII. (5477=
7/50000-m)*Pi*.31172~0.8888888888872114749998 LXVIII. (99613/50000-m)*P=
i*1178~6677.717888888888223875628635565 LXIX. (73623/50000-m)*Pi*12465~50304.8888888884966506526505665 LXX. =
(10317/10000-m)*Pi*2582~6844.8888888889739667966792454 LXXI. (73939/50000-m)*Pi*6506~26385.38170093907888888888051 LXXII. (3644=
7/25000-m)*Pi*703406~2806510.191450719888888888[28digits]5000005500 LXXIII. (2^5/5^3-m)=
*Pi*4.143~
0.8868888888881510150214198 LXXIV. (991/1250-m)/Pi*1=
0428~ 2007.99999999912759129 LXXV. (3127=
/5000-m)*Pi*2198.5~3021.9999999991518540101 LXXVI. (11499/5000-m)*Pi=
*64.654~428.969999999990034987157191279 LXXVII. (1011/500-m)*Pi*25223/2=
~72668.999999999234089 LXXVIII. (3127/5000-m)*Pi*4397/20~
302.199999999915185 LXXIXb . log[m](exp(-m))-4466/39750
~0.000000000519991982697690183242 LXXX. (2711=
7/10000-m)*Pi*26405000~
209362032.199999999991 LXXXI. (16687/1000=
0-m)*Pi*1029~47885.0656599999999905768 LXXXII. (69517/50000-m)*Pi*7004=
11~2645945.056249999999998089072039 LXXXIII. (9569/5000-m)*Pi*700435~
3797899.7411159999999997055115 LXXXIV. (48827/25000-m)*Pi*1161.1~643=
8.99999999957818667 LXXXV. (19349/12500-m)*Pi*.702=
123~2.9999999995734786345744785 LXXXVI. (4638/3125-m)*Pi*702591~28612=
65.0879999999998315604891 LXXXVII. (16687/10000-m)*Pi*10293~47885.0656=
599999999905768 LXXXVIII. &=
nbsp; (3238/3125-m)*Pi*6866~18297.987299999999933137905<=
o:p> LXXXIX. (963/625-m)*Pi*705818E7~ 29999999959955. XC. &=
nbsp; (38471/25000-m)*Pi*706842E7~29999999978997. XCI. &=
nbsp; (4191/10000-m)*Pi*66353/10~4820.29999999911992 XCII. =
(8727/12500-m)*Pi*8281~13275.7336299999999943696339333 XCIII. (21209/25000-m)*Pi*8349~17324.3676192329899999999927873 XCIV. (1.09=
554-m)*Pi*.70137~
1.99999999999 XCV. =
(1.54792-m)*Pi*.702123~2.999999999 XCVI. (1.98=
356-m)*Pi*.709049~3.99999999 XCVII. (10317/1000=
0-m)*Pi*23238~61604.00000000076570117 XCVIII. (591/10000-m)*Pi*=
-27448~
11103.000000000598443547485094 XCIX. (6791/10000-m)*Pi*3598000~ 5552711.00000000005592=
2 C. (2579/5000-m)*Pi*5671E7~ 58425762074.0000000000636 CI. (749/1000-m)*Pi*8189~14436.17866529253000=
000000013055 CII.&=
nbsp; &nbs=
p;
(1167/10000-m)*P=
i*-534E27~119378161735144002723378303931.00000000005023871 CIII. &=
nbsp; 119378161735144002723378303931.00000000005023871 CIV. &=
nbsp; (10317/10000-m)*Pi*580.95~1540.100000000019142529252 CV. &=
nbsp; (1291/500-m)*Pi*665.46~5005.20000000026 CVI. &=
nbsp; (1291/500-m)*Pi*554.55~ 4171.00000000021924384125389=
8 CVII. =
(1291/500-m)*Pi*554.55*4~16684.00000000087697 CVIII. (2579=
/5000-m)*Pi*28355000000~29212881037.0000000000318223 CIX. &=
nbsp; 10^10*(m
+m^(1/2))^50~ 0.4619 CX. &=
nbsp; m^[33]m =
~ 0.4619 CXI. &=
nbsp; m
- 1/7*integral(x^(1/x),x=3D 6.995 .. 8.0004778) ~ 6.79548E-10 CXII. =
sqrt(21*(m-12500000/1290365940577206941)^5+28*Pi+7)~ =
9.7452299999999999999999999999999999 CXIII. sqrt(1+5*Pi+10*(m+sin(125=
/37584486))^15)~4.087537555555555555555559 CXIV. sqrt((9*2+1)*m^(9*2)+9^2)~ 9.0000000000000[42 digits]7777797<=
o:p> CXV. =
sqrt(81*m+10*Pi+11)~ 7.5916110000002877600[=
346
digits]0000006 CXVI. sqrt(97*m^2+24*Pi+2)~ 8.99007644444443419033336334=
23[946
digits]44433 CXVII. sqrt(101*m^12+11*Pi+12)~6.823307070960340277777777[12=
89
digits]777779 CXVIII. sqrt(91*m^4+7*Pi+8)~ 5.486755555557315[1517
digits]55555425 CXIX. sqrt(78*m^5+24*Pi+4)~
8.9115920941302_123456=
78 CXX. =
sqrt(54*m^9+25*Pi+2)~
8.974398702741878899071864371_87654321 Let
C~coth(3.1414*137/42) CXXI. (m^150/15^23)^2 E272~ 1.12162974149 CXXII. (C*2002/133=
47)^23
E19~ 1.12162974149 Let
A~0.11111111139059918350072154839136986358808740782084874... CXXIII. (2002/1483*A)^23 =
E19~ 1.12162974148695338845194143614921855667756257588=
88 CXXIV. (m^150/15^23)^2 E=
272~ 1.12162974148695338845194143614921855667756257588=
88 CXXV. 1499/7047*m=
^(817/31)
~ 1.548089809999999999209209 E-20 CXXVI. 18*m^(817/31) ~
1.310000000261907937956579 E-18 CXXVII. 1056/3901 *m^(183/68)~
0.3007777777777314395065501985 CXXVIII. 9 *m^(183/68)~
0.1000000662878633817200328686 CXXIX. (34/3) E129 *m^178~
6.262087610450000000142446878298305091177204938399999 CXXX. (17/50)
E130*m^178~1.8786262831350000000427340634894915273531614815199999 CXXXI. 136/2289 *m^178 ~
3.2828768600000000000746772
E-131 CXXXII. 884/(189*109) *m^178 ~ 2.37096662111111111116=
504468
E-131 CXXXIII. 782/(105*109) *m^178 ~
3.7753083890000000000858788
E-131 CXXXIV. 68/(63*109) *m^178 ~ 5.47146143333333333345=
77954 E-132 CXXXV. 68/(21*109) *m^178 ~ 1.64143843000000000003=
733863
E-131 CXXXVI. 68/(7 *109) *m^178 ~ 4.92431529000000000011=
20158 E-131 CXXXVII. 68/(1 *109) *m^178 ~ 3.44702070300000000007=
84111 E-130 CXXXVIII. &=
nbsp; 884/(21
*109) *m^178 ~ 2.13386995900000000004=
85402 E-130 CXXXIX. 6800/6867 *m^178 ~ 5.47146143333333333345=
7795 E-130 CXL. =
544/763
*m^178
~
3.9394522320000000000896127
E-130 CXLI. 680/2289
*m^178
~
1.64143843000000000003733 E-130 CXLII. 15640/20601=
*m^178 ~ 4.19478709888888888898=
430984
E-130 CXLIII. 43E39 =
*m^(930/17) ~ CXLIV. 29 =
*m^(244/55) ~
0.017412426867700000002680807 CXLV. 33 =
*m^(7/39) ~ 24.4442300000005593143716657=
9 CXLVI. 87 =
*m^(300/23) ~
0.0000000293617667629999999466439786 CXLVII. .07*(4*m^3+59*m^2+138*m=
)-.629~ =
1.333333333333006036[1019 digits]686477777417 CXLVIII. .04*m^3+5.63*m^2+7.28*m-.5665731~
CXLIX. 85*m^3+580*m^2+79=
8*m~ =
170.944450000000584744821423
CL. &=
nbsp; 93*m^3+364*m^2+958*m~ =
193.4321222222222330557366
CLI. &=
nbsp; 54*m^3+330*m^2+941*m~ =
188.780043733333333310
CLII. =
12*m^3+177*m^2+414*m+15.9~ =
99.99999999999
CLIII. 71*m^3+187*m^2+500*m-1~ =
99.9999999
CLIV. 3*(4*=
m^3+59*m^2+138*m)~ =
84.09999999999
CLV. =
83*m^3+485*m^2+280*m+7.510550474831~
77.77777777777771111111111
CLVI. 10*m^=
3+394*m^2+279*m~ =
66.38388888888822223897571467
CLVII. 39*m^3+134*=
m^2+159*m~ =
34.8572722450999999999
CLVIII. .6*(4*m^3+59*m^2+=
138*m+.3)~ =
16.9999999999971945956
CLIX. 10*m^3+139*m^2+723*m~ =
140.7943025992222222220463012
CLX. =
13*m^3+195*m^2+859*m~ =
168.3394131111111112531981521
CLXI. 81*m^3+976*m^2+921*m+792~ =
999.999999945290
CLXII. 95*m^3+993*=
m^2+385*m-8~ =
99.9999999651918979
CLXIII. 10*m^3+789*m^2+42=
1*m-7~ =
99.99999999856215157258758960
CLXIV. 12*m^3+670*m^2+28=
2*m+1.07~ =
77.771111111119129159
CLXV. 31*m^3+636*=
m^2+147*m-16.93279~ =
33.33333325333333333866206
CLXVI. 31*m^3+728*m^2+98=
0*m+790~ =
999.99999998870500815065
CLXVII. 20*m^3+788*m^2+558*m+64=
5~ =
777.767777777776444477
CLXVIII. 20*m^3+295*m^2+690*m+526.5~ =
666.66666666664328829669780
CLXIX. 16*m^3+729*m^2+42=
0*m+339.71~ =
444.4444444444477868186118688
CLXX. 92*m^3+701*=
m^2+761*m-57.1991814~
111.1111111111111111887830831
CLXXI. 85*m^3+272*m^2+54=
2*m~ =
111.98267798779088888888873737
CLXXII. 45*m^3+745*m^2+444*m~
CLXXIII. 80*m^3+701*m^2+467*m-3~ =
110.0000000186508900879866858
CLXXIV. 32*m^3+224*m^2+259*m-6.77303996~
CLXXV. 67*m^3+226*m^2+165*m-.0=
0574797332686~ 39.4111111111111111111111195=
3
CLXXVI. 4*m^3+59*m^2+138*m+5.3~ =
33.333333333328[1326 digits]4604690808000
CLXXVII. .02*(1001*m^2+25*m+2.58375203781+83/m+8/m=
^2)~
14.222222222222240222222222
CLXXVIII. &=
nbsp; 1065*m^2+6*m-208.49544+99/m+7/m^2~ =
555.55555555888888888390109
CLXXIX. .042*m^2+.112*m+.7381+.029/m+=
.003/m^2~ =
1.0000000000086681088616
CLXXX. .0609*m^2+.098*m+.8864+=
.0063/m+.0021/m^2~ =
0.9999999999991521099
CLXXXI. .03/80*(28*m^2+127*m-163+55/m=
+5/m^2)~ =
0.111111111111148684099
CLXXXII. .27/80*(-163+5/m^2+55/m+127*m+28*m^2-41.6=
397974*m^16)~
0.999999999999999999999999
CLXXXIII. &=
nbsp; 113*m^2+253*m-6.4676551+5/m+1/m^2~
100.0000000001900000000564070
CLXXXIV. &=
nbsp; 137*m^2+148*m-45.4+24/m+3/m^2~ =
200.0000000000522
CLXXXV. 191*m^2+238*m+477+46/m+8/m^2~ =
1000.0000000146490190
CLXXXVI. &=
nbsp; 160*m^2+95*m+314+61/m+8/m^2~ =
888.88888885188208
CLXXXVII. &=
nbsp; 2*(705*m^2+28*m+54/m+4/m^2)~ =
861.8632044910000000052105089
CLXXXVIII. =
3*(819*m^2+45*m+12/m+7/m^2)+404.99/4~ 1000.000000000000422
CLXXXIX. &=
nbsp; 3*(819*m^2+45*m+12/m+7/m^2)~ =
898.7525000000004228495978576
CXC. 199*m^2+2*m+155.6174226+68/m+5/m^2~
666.666666666666666
CXCI. 175*m=
^2+82*m-82.5066051+63/m+6/m^2~
444.444444444444444645794
CXCII. 3/5*(921*m^=
2+41*m+87/m+7/m^2)~ =
421.0000000060305662204104732
CXCIII. 7*(920*m^2+3*m+77=
/m+7/m^2)~ =
4488.83034700000000811848
CXCIV. 7*(622*m^2+7*m+19/m+10/=
m^2)~ =
2854.333333336643129342817728
CXCV. 8*(819*m^2+=
45*m+12/m+7/m^2)~ =
2396.673333333334460932260954
CXCVI. 8*(805*m^2+4*m-312.5187=
5+74/m+1/m^2)~
1111.111111111507619155806615
CXCVII. 6/5*(819*m^2+45*m+.5+12/m+7/m=
^2)~
360.10100000000016913983914
CXCVIII. 2/3*(819*m^2+45*m-131.67/4+12/m+7/m=
^2)~ 177.777777777777871744355079=
5
CXCIX. 127*m^2+40*m+146+=
1/m+6/m^2~ =
333.333333363
CC. &=
nbsp; .003*(805*m^2+20*m-299/6+34/m+6/m^2)~
1.00000000007527022828441
CCI. &=
nbsp; .0018*(805*m^2+35*m-250.7926785+97/m+9/m^2)~1.0000000000000000=
0477249
CCII. .001*(m^2+81*m+240+92/m+9/m^2)~ =
1.00000000097744
CCIII. 4*(34=
*m^2+35*m+1836.25+70/m+10/m^2)~ 9999.99999999042=
022
CCIV. 4*(72=
*m^2+35*m+67/m+3/m^2)~ =
1803.08888888881913
CCV. 4/3*(83*m^2+29*m-542+63/m+7/m^2)~ =
0.111111112265225
CCVI. 141*m=
^2+75*m+740+8/m+7/m^2~ =
999.9999993001829
CCVII. 205/18/(m^2=
+(3.36951)^2)~ =
1.00000000030933
CCVIII. 82/(m^2+(3.36951)^2)~
CCIX. 42/(m=
^2+1.78759^2)~ =
&nb=
sp;
12.99999990908
CCX. 47/(m^2+(3.72409)^2)~ =
&nb=
sp;
3.3802887631111111188556966
CCXI. 28/(m=
^2+(6.0653)^2)~ =
&nb=
sp;
0.760391111111112891
CCXIIc.
b:=3D1.92:evalf(log[b](log[b]=
(log[b](log[b](log[b](4279))))))-m
~-0.000002866507074428479684637928
CCXIII. 2/(m^2+1.1329^2)~=
=
&nb=
sp;
1.5165834741111111167
CCXIV. 7/(m^2+6.0653^2)~ =
&nb=
sp;
0.19009777777777822287
CCXV. 10/81-4/(m^=
2+5.689^2)~ =
&nb=
sp;
0.00000004666
CCXVI. 1246705*m~
234205.555555671
CCXVII. 1320800 *m~
248125.0157638982524242424
CCXVIII. 1356070 *m~
254750.82535353535
CCXIX. 1381443 *m~