Errors, E101+E102, Errors

Leonhard Euler (1707-1783)

Chap.VI
Exponentialibus ac Logarithmis

Z=5.000000
lZ = 0.698970 (correct value)

E101 p.77

0.3010300...=log(2)/log(10)

0.3010299(correct value)
+0.0000001

1/0.30103...=log(10)/log(2)

3.321980(correct value)
3.321977(p.77 in E101)
-0.000003

E101 p.90 p.91

e

2.71828182845904523536028 (the last number is correct)
2.71828182845904523536028747135266249775724709
Round down

log n

Chap.VII
l7 +0.0000000000000000000001112
l8 +0.0000000000000000000000001
l9 +0.0000000000000000000000001

E101 p.99 p.100 p.101

sin(m/n pi/2)

01 -0.0000000000000000000000000000
03 +0.0000000000000000000000000002
05 -0.0000000000000000000000000006
07 +0.0000000000000000000000000007
09 -0.0000000000000000000000000003
11 +0.0000000000000000000000000005
13 -0.0000000000000000000000000006
15 +0.0000000000000000000000000008
17 -0.0000000000000000000000000006
19 +0.0000000000000000000000000004
21 -0.0000000000000000000000000004
23 +0.0000000000000000000000000002
25 -0.0000000000000000000000000001
27 +0.0000000000000000000000000000
29 -0.0000000000000000000000000001

cos(m/n pi/2)

00 -0.0000000000000000000000000000
02 +0.0000000000000000000000000004
04 -0.0000000000000000000000000004
06 +0.0000000000000000000000000008
08 -0.0000000000000000000000000004
10 +0.0000000000000000000000000004
12 -0.0000000000000000000000000005
14 +0.0000000000000000000000000002
16 -0.0000000000000000000000000006
18 +0.0000000000000000000000000003
20 -0.0000000000000000000000000005
22 +0.0000000000000000000000000003
24 -0.0000000000000000000000000003
26 -0.0000000000000000000000000001
28 -0.0000000000000000000000000002
30 +0.0000000000000000000000000002

E101 p.102

tan(m/n pi/2)

05 -0.0000000000001
07 -0.0000000000001
09 -0.0000000000128
11 +0.0000000000001
13 -0.0000000000001

cot(m/n pi/2)

05 -0.0000000000001
11 -0.0000000000001

E101 p.131 p.150 p.151 E212 p.335 p.336 E352 p.87 p.88

zeta(2n)(1-1/2^(2n))

E 05 +0.00000000000000000001998

E101 p.153 p.154

E 05 +0.00000000000000000001998

zeta(2n)/2^(2n)

05 +0.00000000000000000000002
06 +0.00000000000000000000001
07 +0.00000000000000000000000

08 -0.00000000000000000001526
11 -0.00000000000000000000101
16 -0.00000000000000000000001
21 -0.00000000000000000000001
24 -0.00000000000000000000001

13=E5+8 +0.00000000000000000000472

E101 p.237 p.238

the sum of 1/p^(2n)

02 0.452247420041065 +157
04 0.076993139764246 +006
06 0.017070086850637 +002
08 0.004061405366518 -003
10 0.000993603574437 -804
12 0.000246026470035 -002
14 0.000061244396725 ----
16 0.000015282026219 ----
18 0.000003817278702 ----
20 0.000000953961124 -001
22 0.000000238450446 ----
24 0.000000059608184 ----
26 0.000000014901555 ----
28 0.000000003725333 ----
30 0.000000000931326 -003
32 0.000000000232830 ----
34 0.000000000058207 ----
36 0.000000000014551 ----

p.289

l.y=sqrt(2)
1.41421356 (correct value)
1.4142 356 (p.289 in E102)

log(2^sqrt(2))/log(10)
+0.0000067=0.4257274-0.4257207

2^sqrt(2)
+0.000042=2.665186-2.665144

10^sqrt(2)
+0.001317=25.955870-25.954553

p.290

cos l2

-0.00000000000989=0.76923890135408-0.76923890136397

p.151(E101) p.307(E102)

log pi

1.1447298858494001741434273 (correct value)
1.14472988584940017414342-- (p.151 in E101)
1.1447298858494001741434237 (p.307 in E102)

p.309

sin 1

-0.00000000000275=0.84147098480514-0.84147098480789

p.309

cos 1

-0.00000000002472=0.54030230584341-0.54030230586813

p.323 p.324

s+cot s=(2n+1)pi/2

03 +0.00000001
05 +0.00000001
07 +0.00000002
09 +0.00000005

Solutions
EP: 7 EP: 37 EP: 73
Computations
UBASIC Program: E101-1.UB E101-2.UB E101-3.UB
E101-A.UB E101-B.UB E101-C.UB E102.UB

Reg: 2007, Jan. 29
Title: Errors, E101+E102, Errors
Method: webpage
Content:
https://math0.pm.tokushima-u.ac.jp/~hiroki/major/euler7.html
EP: 149

Index