Singularities of Møller-Plesset series: example "a30"

Molecule BH. Basis aug-cc-pVTZ. Structure "mpn_Rfci"

Content

• Definition of quadratic approximants
  • Approximant [6, 6, 5]
  • Approximant [6, 6, 6]
  • Approximant [7, 6, 6]
  • Approximant [7, 7, 6]
  • Approximant [7, 7, 7]
  • Approximant [8, 7, 7]
  • Approximant [8, 8, 7]
  • Approximant [8, 8, 8]
  • Approximant [9, 8, 8]
  • Approximant [9, 9, 8]
  • Approximant [9, 9, 9]
  • Approximant [10, 9, 9]
  • Approximant [10, 10, 9]
  • Approximant [10, 10, 10]
  • Approximant [11, 10, 10]
  • Approximant [11, 11, 10]
  • Approximant [11, 11, 11]
  • Approximant [12, 11, 11]
  • Approximant [12, 12, 11]
  • Approximant [12, 12, 12]

Plot of singularities

List of examples

Mathematica programs

Work in UMassD

Unpublished reports

Quadratic approximants

[n₁, n₂, n₃] approximant is defined as a solution of the quadratic equation
A(z)f² +  B(z)f +  C(z) = 0
with polynomial coefficients A(z), B(z) and C(z) of degree n₃, n₂ and n₁ respectively.

Square-root singularities are determined as zeroes of the discriminant
D(z) = B²(z) - 4A(z)C(z).
The weight c of the singularity z_c is defined so that
f ~ c(1 - z/z_c)^1/2 at z -> z_c.
The weight is calculated by formula
c = 1/2[-z(D/A²)']^1/2
where r. h. s. of the above equation is evaluated at z = z_c.

Table 1. Singularities with their weights for the quadratic approximant [6, 6, 5] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	1.4297 + 0.022 i	0.101 - 0.137 i
2	1.4297 - 0.022 i	0.101 + 0.137 i
3	1.6579 + 0.4269 i	0.176 + 0.157 i
4	1.6579 - 0.4269 i	0.176 - 0.157 i
5	2.4747	8.67
6	-2.9675	0.00524
7	-2.7124 + 1.6161 i	0.000715 + 0.0049 i
8	-2.7124 - 1.6161 i	0.000715 - 0.0049 i
9	-2.7035 + 2.1193 i	0.00663 - 0.00088 i
10	-2.7035 - 2.1193 i	0.00663 + 0.00088 i
11	18.0867	4.45 i
12	-57.7998	1.46 i

  Top of the page    

Table 2. Singularities with their weights for the quadratic approximant [6, 6, 6] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	0.2544 + 0.e-5 i	6.27e-8 - 6.27e-8 i
2	0.2544 - 0.e-5 i	6.27e-8 + 6.27e-8 i
3	1.4488	0.139
4	1.5142	0.765 i
5	1.6549 + 0.4684 i	0.0684 + 0.111 i
6	1.6549 - 0.4684 i	0.0684 - 0.111 i
7	2.5653	5.24e4
8	-2.8514 + 0.814 i	0.004 + 0.00279 i
9	-2.8514 - 0.814 i	0.004 - 0.00279 i
10	-3.2502 + 1.5582 i	0.00425 - 0.0069 i
11	-3.2502 - 1.5582 i	0.00425 + 0.0069 i
12	-6.5728	0.235

  Top of the page    

Table 3. Singularities with their weights for the quadratic approximant [7, 6, 6] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.4278 + 0.e-5 i	3.68e-7 + 3.68e-7 i
2	-0.4278 - 0.e-5 i	3.68e-7 - 3.68e-7 i
3	1.3852	0.0349
4	1.4994	0.0931 i
5	1.5775 + 0.4526 i	0.0601 + 0.0246 i
6	1.5775 - 0.4526 i	0.0601 - 0.0246 i
7	-3.0933	0.0158
8	-2.2854 + 2.8671 i	0.00722 - 0.00361 i
9	-2.2854 - 2.8671 i	0.00722 + 0.00361 i
10	3.9442 + 1.1436 i	0.183 - 0.199 i
11	3.9442 - 1.1436 i	0.183 + 0.199 i
12	-3.7911 + 2.7039 i	0.000483 + 0.00862 i
13	-3.7911 - 2.7039 i	0.000483 - 0.00862 i

  Top of the page    

Table 4. Singularities with their weights for the quadratic approximant [7, 7, 6] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.2539 + 0.4889 i	2.44e-7 + 4.e-8 i
2	-0.2539 - 0.4889 i	2.44e-7 - 4.e-8 i
3	-0.2539 + 0.4889 i	4.e-8 - 2.44e-7 i
4	-0.2539 - 0.4889 i	4.e-8 + 2.44e-7 i
5	1.0336 + 0.0022 i	0.000139 - 0.000137 i
6	1.0336 - 0.0022 i	0.000139 + 0.000137 i
7	1.4468	0.0193
8	1.8305 + 0.697 i	0.0404 + 0.0382 i
9	1.8305 - 0.697 i	0.0404 - 0.0382 i
10	-2.3396 + 0.6743 i	0.000511 + 0.000222 i
11	-2.3396 - 0.6743 i	0.000511 - 0.000222 i
12	-3.6688	0.00131
13	-6.5053	0.0178 i
14	14.9597	4.58 i

  Top of the page    

Table 5. Singularities with their weights for the quadratic approximant [7, 7, 7] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.6159 + 0.e-5 i	2.25e-7 + 2.25e-7 i
2	-0.6159 - 0.e-5 i	2.25e-7 - 2.25e-7 i
3	1.4167	0.0233
4	-0.1364 + 1.5203 i	0.0000567 - 0.0000396 i
5	-0.1364 - 1.5203 i	0.0000567 + 0.0000396 i
6	-0.1372 + 1.5298 i	0.0000395 + 0.0000577 i
7	-0.1372 - 1.5298 i	0.0000395 - 0.0000577 i
8	1.5602 + 0.634 i	0.006 - 0.0148 i
9	1.5602 - 0.634 i	0.006 + 0.0148 i
10	2.2502	0.168 i
11	-2.4368 + 0.7254 i	0.000599 + 0.0000455 i
12	-2.4368 - 0.7254 i	0.000599 - 0.0000455 i
13	-4.5002	0.00475
14	9.9755	1.57

  Top of the page    

Table 6. Singularities with their weights for the quadratic approximant [8, 7, 7] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.6273 + 0.e-5 i	2.86e-7 + 2.86e-7 i
2	-0.6273 - 0.e-5 i	2.86e-7 - 2.86e-7 i
3	1.4176	0.0237
4	-0.045 + 1.5312 i	0.0000464 - 0.0000671 i
5	-0.045 - 1.5312 i	0.0000464 + 0.0000671 i
6	-0.0417 + 1.5399 i	0.0000679 + 0.0000472 i
7	-0.0417 - 1.5399 i	0.0000679 - 0.0000472 i
8	1.5612 + 0.6323 i	0.00582 - 0.0152 i
9	1.5612 - 0.6323 i	0.00582 + 0.0152 i
10	2.2205	0.173 i
11	-2.5566 + 0.7565 i	0.000884 - 0.0000102 i
12	-2.5566 - 0.7565 i	0.000884 + 0.0000102 i
13	7.1154	71.4
14	-8.011 + 2.832 i	0.0584 + 0.0762 i
15	-8.011 - 2.832 i	0.0584 - 0.0762 i

  Top of the page    

Table 7. Singularities with their weights for the quadratic approximant [8, 8, 7] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	0.1674	0
2	0.1674	0
3	-0.6678	6.3e-7
4	-0.6678	6.3e-7 i
5	1.4139	0.0188
6	1.5706 + 0.731 i	0.0103 - 0.00376 i
7	1.5706 - 0.731 i	0.0103 + 0.00376 i
8	0.8027 + 1.8393 i	0.000814 - 0.0000936 i
9	0.8027 - 1.8393 i	0.000814 + 0.0000936 i
10	0.903 + 1.9347 i	0.0000916 + 0.00099 i
11	0.903 - 1.9347 i	0.0000916 - 0.00099 i
12	-2.8947	0.00439
13	-2.6815 + 3.7051 i	0.0134 + 0.00405 i
14	-2.6815 - 3.7051 i	0.0134 - 0.00405 i
15	-4.9868	0.0219 i
16	11.6828	0.398 i

  Top of the page    

Table 8. Singularities with their weights for the quadratic approximant [8, 8, 8] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.1085 + 0.6476 i	1.09e-7 - 2.15e-7 i
2	-0.1085 - 0.6476 i	1.09e-7 + 2.15e-7 i
3	-0.1085 + 0.6476 i	2.15e-7 + 1.09e-7 i
4	-0.1085 - 0.6476 i	2.15e-7 - 1.09e-7 i
5	-1.0572 + 0.4279 i	6.99e-7 - 1.16e-6 i
6	-1.0572 - 0.4279 i	6.99e-7 + 1.16e-6 i
7	-1.0629 + 0.4191 i	1.14e-6 + 6.98e-7 i
8	-1.0629 - 0.4191 i	1.14e-6 - 6.98e-7 i
9	1.4214	0.0316
10	1.5569 + 0.5709 i	0.00504 + 0.0208 i
11	1.5569 - 0.5709 i	0.00504 - 0.0208 i
12	1.8458	1.34 i
13	-1.7293 + 0.6455 i	0.0000238 - 0.0000129 i
14	-1.7293 - 0.6455 i	0.0000238 + 0.0000129 i
15	-2.036	0.0000297
16	4.9725	0.758

  Top of the page    

Table 9. Singularities with their weights for the quadratic approximant [9, 8, 8] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.1036 + 0.69 i	1.62e-7 - 3.e-7 i
2	-0.1036 - 0.69 i	1.62e-7 + 3.e-7 i
3	-0.1036 + 0.6901 i	3.e-7 + 1.62e-7 i
4	-0.1036 - 0.6901 i	3.e-7 - 1.62e-7 i
5	-0.8547 + 0.427 i	2.49e-8 - 6.63e-7 i
6	-0.8547 - 0.427 i	2.49e-8 + 6.63e-7 i
7	-0.8558 + 0.4266 i	6.63e-7 + 2.62e-8 i
8	-0.8558 - 0.4266 i	6.63e-7 - 2.62e-8 i
9	1.4232	0.0343
10	1.5581 + 0.5622 i	0.00728 + 0.0214 i
11	1.5581 - 0.5622 i	0.00728 - 0.0214 i
12	1.8046	3.66 i
13	-1.9453 + 0.728 i	0.0000737 - 0.0000352 i
14	-1.9453 - 0.728 i	0.0000737 + 0.0000352 i
15	-2.7579	0.000227
16	4.5572	0.626
17	-46.3729	0.179 i

  Top of the page    

Table 10. Singularities with their weights for the quadratic approximant [9, 9, 8] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.0572 + 0.6864 i	1.94e-7 - 5.62e-9 i
2	-0.0572 - 0.6864 i	1.94e-7 + 5.62e-9 i
3	-0.0572 + 0.6864 i	5.61e-9 + 1.94e-7 i
4	-0.0572 - 0.6864 i	5.61e-9 - 1.94e-7 i
5	-0.7467 + 0.3531 i	1.26e-8 - 2.01e-7 i
6	-0.7467 - 0.3531 i	1.26e-8 + 2.01e-7 i
7	-0.7469 + 0.3529 i	2.01e-7 + 1.27e-8 i
8	-0.7469 - 0.3529 i	2.01e-7 - 1.27e-8 i
9	1.4405	0.0549
10	1.5293 + 0.5604 i	0.00907 + 0.013 i
11	1.5293 - 0.5604 i	0.00907 - 0.013 i
12	1.8201	1.58 i
13	-2.1835 + 0.9826 i	0.0000748 - 0.000178 i
14	-2.1835 - 0.9826 i	0.0000748 + 0.000178 i
15	-3.0645 + 4.0175 i	0.000215 + 0.00444 i
16	-3.0645 - 4.0175 i	0.000215 - 0.00444 i
17	4.4049 + 5.3288 i	0.0593 + 0.00741 i
18	4.4049 - 5.3288 i	0.0593 - 0.00741 i

  Top of the page    

Table 11. Singularities with their weights for the quadratic approximant [9, 9, 9] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	0.2904	4.63e-10
2	0.2904	4.63e-10 i
3	-0.0998 + 0.7068 i	3.89e-8 + 2.42e-7 i
4	-0.0998 - 0.7068 i	3.89e-8 - 2.42e-7 i
5	-0.0998 + 0.7068 i	2.42e-7 - 3.89e-8 i
6	-0.0998 - 0.7068 i	2.42e-7 + 3.89e-8 i
7	-0.8206 + 0.4201 i	7.34e-8 + 3.7e-7 i
8	-0.8206 - 0.4201 i	7.34e-8 - 3.7e-7 i
9	-0.8216 + 0.4197 i	3.7e-7 - 7.26e-8 i
10	-0.8216 - 0.4197 i	3.7e-7 + 7.26e-8 i
11	1.4077	0.0221
12	1.5798 + 0.5686 i	0.00113 + 0.0296 i
13	1.5798 - 0.5686 i	0.00113 - 0.0296 i
14	1.8407	1.93 i
15	-1.9665 + 0.7729 i	0.0000668 - 0.000053 i
16	-1.9665 - 0.7729 i	0.0000668 + 0.000053 i
17	-2.967	0.000344
18	4.3754	0.541

  Top of the page    

Table 12. Singularities with their weights for the quadratic approximant [10, 9, 9] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.0505 + 0.9211 i	1.27e-7 + 7.6e-8 i
2	-0.0505 - 0.9211 i	1.27e-7 - 7.6e-8 i
3	-0.0511 + 0.9234 i	7.77e-8 - 1.27e-7 i
4	-0.0511 - 0.9234 i	7.77e-8 + 1.27e-7 i
5	-0.4985 + 0.8071 i	3.47e-8 - 6.74e-8 i
6	-0.4985 - 0.8071 i	3.47e-8 + 6.74e-8 i
7	-0.5035 + 0.8064 i	6.72e-8 + 3.53e-8 i
8	-0.5035 - 0.8064 i	6.72e-8 - 3.53e-8 i
9	-1.2513 + 0.248 i	2.08e-7 + 3.17e-7 i
10	-1.2513 - 0.248 i	2.08e-7 - 3.17e-7 i
11	1.3084 + 0.2478 i	0.0000347 + 0.00106 i
12	1.3084 - 0.2478 i	0.0000347 - 0.00106 i
13	1.3379 + 0.3934 i	0.000353 + 0.00113 i
14	1.3379 - 0.3934 i	0.000353 - 0.00113 i
15	-1.4759 + 0.0205 i	1.48e-7 + 1.23e-7 i
16	-1.4759 - 0.0205 i	1.48e-7 - 1.23e-7 i
17	-1.145 + 1.8434 i	0.0000206 - 0.0000143 i
18	-1.145 - 1.8434 i	0.0000206 + 0.0000143 i
19	11.9989	0.156

  Top of the page    

Table 13. Singularities with their weights for the quadratic approximant [10, 10, 9] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.4539 + 0.5762 i	1.94e-9 - 7.08e-9 i
2	-0.4539 - 0.5762 i	1.94e-9 + 7.08e-9 i
3	-0.4537 + 0.5765 i	7.09e-9 + 1.93e-9 i
4	-0.4537 - 0.5765 i	7.09e-9 - 1.93e-9 i
5	-0.7491 + 0.1846 i	2.6e-9 + 5.15e-9 i
6	-0.7491 - 0.1846 i	2.6e-9 - 5.15e-9 i
7	-0.7501 + 0.1845 i	5.17e-9 - 2.59e-9 i
8	-0.7501 - 0.1845 i	5.17e-9 + 2.59e-9 i
9	-0.0174 + 0.831 i	4.5e-8 + 4.91e-8 i
10	-0.0174 - 0.831 i	4.5e-8 - 4.91e-8 i
11	-0.0172 + 0.8317 i	4.94e-8 - 4.51e-8 i
12	-0.0172 - 0.8317 i	4.94e-8 + 4.51e-8 i
13	1.254 + 0.2117 i	0.000287 + 0.000383 i
14	1.254 - 0.2117 i	0.000287 - 0.000383 i
15	1.3451 + 0.3132 i	0.00108 + 0.000305 i
16	1.3451 - 0.3132 i	0.00108 - 0.000305 i
17	-2.3386 + 1.6715 i	0.000163 - 0.000156 i
18	-2.3386 - 1.6715 i	0.000163 + 0.000156 i
19	3.382	0.565
20	19.704	2.22 i

  Top of the page    

Table 14. Singularities with their weights for the quadratic approximant [10, 10, 10] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.3427 + 0.7428 i	4.7e-9 + 3.51e-8 i
2	-0.3427 - 0.7428 i	4.7e-9 - 3.51e-8 i
3	-0.3426 + 0.7436 i	3.51e-8 - 4.71e-9 i
4	-0.3426 - 0.7436 i	3.51e-8 + 4.71e-9 i
5	0.0856 + 0.9185 i	1.95e-7 - 9.24e-9 i
6	0.0856 - 0.9185 i	1.95e-7 + 9.24e-9 i
7	0.087 + 0.9184 i	1.03e-8 + 1.96e-7 i
8	0.087 - 0.9184 i	1.03e-8 - 1.96e-7 i
9	-1.0382 + 0.3901 i	1.84e-7 + 7.37e-9 i
10	-1.0382 - 0.3901 i	1.84e-7 - 7.37e-9 i
11	-1.0444 + 0.4135 i	1.07e-9 + 1.93e-7 i
12	-1.0444 - 0.4135 i	1.07e-9 - 1.93e-7 i
13	1.3528 + 0.2502 i	0.00043 - 0.00195 i
14	1.3528 - 0.2502 i	0.00043 + 0.00195 i
15	1.3651 + 0.435 i	0.000519 - 0.0016 i
16	1.3651 - 0.435 i	0.000519 + 0.0016 i
17	-1.6308 + 1.3208 i	0.0000166 - 0.0000187 i
18	-1.6308 - 1.3208 i	0.0000166 + 0.0000187 i
19	4.7439	1.59
20	-5.2008	0.106

  Top of the page    

Table 15. Singularities with their weights for the quadratic approximant [11, 10, 10] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	0.0283	0
2	0.0283	0
3	-0.3549 + 0.7407 i	7.32e-9 + 2.02e-8 i
4	-0.3549 - 0.7407 i	7.32e-9 - 2.02e-8 i
5	-0.3552 + 0.7418 i	2.02e-8 - 7.31e-9 i
6	-0.3552 - 0.7418 i	2.02e-8 + 7.31e-9 i
7	0.0731 + 0.9268 i	1.32e-7 - 4.84e-8 i
8	0.0731 - 0.9268 i	1.32e-7 + 4.84e-8 i
9	0.0751 + 0.9275 i	4.94e-8 + 1.33e-7 i
10	0.0751 - 0.9275 i	4.94e-8 - 1.33e-7 i
11	-1.0067 + 0.3618 i	8.98e-8 + 3.4e-9 i
12	-1.0067 - 0.3618 i	8.98e-8 - 3.4e-9 i
13	-1.0182 + 0.3815 i	9.57e-8 i
14	-1.0182 - 0.3815 i	-9.57e-8 i
15	1.3693 + 0.2535 i	0.000657 - 0.00253 i
16	1.3693 - 0.2535 i	0.000657 + 0.00253 i
17	1.3607 + 0.4401 i	0.000453 - 0.00161 i
18	1.3607 - 0.4401 i	0.000453 + 0.00161 i
19	-1.5381 + 1.5761 i	9.44e-6 + 0.0000237 i
20	-1.5381 - 1.5761 i	9.44e-6 - 0.0000237 i
21	14.2055	0.155

  Top of the page    

Table 16. Singularities with their weights for the quadratic approximant [11, 11, 10] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.8654 + 0.1615 i	3.92e-8 + 5.06e-8 i
2	-0.8654 - 0.1615 i	3.92e-8 - 5.06e-8 i
3	-0.8663 + 0.1625 i	5.09e-8 - 3.93e-8 i
4	-0.8663 - 0.1625 i	5.09e-8 + 3.93e-8 i
5	-0.4731 + 0.7593 i	9.99e-8 - 7.08e-8 i
6	-0.4731 - 0.7593 i	9.99e-8 + 7.08e-8 i
7	-0.4722 + 0.7605 i	7.1e-8 + 9.98e-8 i
8	-0.4722 - 0.7605 i	7.1e-8 - 9.98e-8 i
9	-0.063 + 0.993 i	4.13e-7 - 8.85e-8 i
10	-0.063 - 0.993 i	4.13e-7 + 8.85e-8 i
11	-0.066 + 0.9953 i	8.3e-8 + 4.13e-7 i
12	-0.066 - 0.9953 i	8.3e-8 - 4.13e-7 i
13	1.3754 + 0.5234 i	0.00198 - 0.000523 i
14	1.3754 - 0.5234 i	0.00198 + 0.000523 i
15	1.5194 + 0.2476 i	0.0201 - 0.00555 i
16	1.5194 - 0.2476 i	0.0201 + 0.00555 i
17	0.618 + 1.8043 i	0.0000661 + 0.0000298 i
18	0.618 - 1.8043 i	0.0000661 - 0.0000298 i
19	0.368 + 1.8769 i	0.0000438 - 0.0000228 i
20	0.368 - 1.8769 i	0.0000438 + 0.0000228 i
21	-2.4905	0.000475
22	-6.4821	0.0147 i

  Top of the page    

Table 17. Singularities with their weights for the quadratic approximant [11, 11, 11] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.7353	6.02e-10
2	-0.7361	6.01e-10 i
3	-0.46 + 0.757 i	1.01e-8 - 7.35e-9 i
4	-0.46 - 0.757 i	1.01e-8 + 7.35e-9 i
5	-0.4556 + 0.7608 i	7.56e-9 + 1.01e-8 i
6	-0.4556 - 0.7608 i	7.56e-9 - 1.01e-8 i
7	-0.0479 + 0.9828 i	6.35e-8 - 3.57e-8 i
8	-0.0479 - 0.9828 i	6.35e-8 + 3.57e-8 i
9	-0.0562 + 0.9891 i	3.2e-8 + 6.44e-8 i
10	-0.0562 - 0.9891 i	3.2e-8 - 6.44e-8 i
11	-0.9872 + 0.2184 i	8.52e-9 + 4.97e-9 i
12	-0.9872 - 0.2184 i	8.52e-9 - 4.97e-9 i
13	-1.0264 + 0.1929 i	7.89e-9 - 7.44e-9 i
14	-1.0264 - 0.1929 i	7.89e-9 + 7.44e-9 i
15	1.3634 + 0.5083 i	0.00104 - 0.00137 i
16	1.3634 - 0.5083 i	0.00104 + 0.00137 i
17	1.6286 + 0.1791 i	0.208 + 0.1 i
18	1.6286 - 0.1791 i	0.208 - 0.1 i
19	0.8234 + 1.6764 i	0.0000393 - 0.0000161 i
20	0.8234 - 1.6764 i	0.0000393 + 0.0000161 i
21	0.3448 + 2.1328 i	0.0000295 + 5.93e-6 i
22	0.3448 - 2.1328 i	0.0000295 - 5.93e-6 i

  Top of the page    

Table 18. Singularities with their weights for the quadratic approximant [12, 11, 11] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	0.3742 + 0.e-5 i	0
2	0.3742 - 0.e-5 i	0
3	-0.8607 + 0.163 i	5.e-10 + 5.e-9 i
4	-0.8607 - 0.163 i	5.e-10 - 5.e-9 i
5	-0.8655 + 0.1575 i	5.01e-9 - 3.42e-10 i
6	-0.8655 - 0.1575 i	5.01e-9 + 3.42e-10 i
7	-0.4728 + 0.7646 i	6.21e-9 - 8.98e-9 i
8	-0.4728 - 0.7646 i	6.21e-9 + 8.98e-9 i
9	-0.4812 + 0.7631 i	8.91e-9 + 6.46e-9 i
10	-0.4812 - 0.7631 i	8.91e-9 - 6.46e-9 i
11	-0.0648 + 0.9977 i	3.96e-8 + 2.41e-8 i
12	-0.0648 - 0.9977 i	3.96e-8 - 2.41e-8 i
13	-0.0739 + 1.0164 i	2.82e-8 - 3.85e-8 i
14	-0.0739 - 1.0164 i	2.82e-8 + 3.85e-8 i
15	1.3362 + 0.4845 i	0.000113 - 0.000837 i
16	1.3362 - 0.4845 i	0.000113 + 0.000837 i
17	1.5977 + 0.127 i	0.731 + 0.425 i
18	1.5977 - 0.127 i	0.731 - 0.425 i
19	0.0672 + 1.6865 i	1.53e-6 + 2.32e-6 i
20	0.0672 - 1.6865 i	1.53e-6 - 2.32e-6 i
21	0.4688 + 1.6413 i	3.7e-6 + 6.05e-6 i
22	0.4688 - 1.6413 i	3.7e-6 - 6.05e-6 i
23	-5.4507	0.00931

  Top of the page    

Table 19. Singularities with their weights for the quadratic approximant [12, 12, 11] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.0273 + 0.6909 i	1.62e-10 - 1.1e-10 i
2	-0.0273 - 0.6909 i	1.62e-10 + 1.1e-10 i
3	-0.0271 + 0.691 i	1.1e-10 + 1.62e-10 i
4	-0.0271 - 0.691 i	1.1e-10 - 1.62e-10 i
5	-0.4891 + 0.7283 i	1.96e-9 + 1.9e-10 i
6	-0.4891 - 0.7283 i	1.96e-9 - 1.9e-10 i
7	-0.8582 + 0.196 i	9.65e-10 + 1.5e-9 i
8	-0.8582 - 0.196 i	9.65e-10 - 1.5e-9 i
9	-0.4791 + 0.7417 i	-1.99e-9 i
10	-0.4791 - 0.7417 i	1.99e-9 i
11	-0.8718 + 0.1882 i	1.62e-9 - 9.01e-10 i
12	-0.8718 - 0.1882 i	1.62e-9 + 9.01e-10 i
13	-0.0799 + 0.9297 i	3.79e-9 + 1.73e-9 i
14	-0.0799 - 0.9297 i	3.79e-9 - 1.73e-9 i
15	-0.0504 + 0.9351 i	1.01e-9 - 4.6e-9 i
16	-0.0504 - 0.9351 i	1.01e-9 + 4.6e-9 i
17	1.3175 + 0.2559 i	0.000351 - 0.000169 i
18	1.3175 - 0.2559 i	0.000351 + 0.000169 i
19	1.2223 + 0.7092 i	0.000032 - 0.0000304 i
20	1.2223 - 0.7092 i	0.000032 + 0.0000304 i
21	1.2252 + 1.122 i	0.0000291 + 0.0000194 i
22	1.2252 - 1.122 i	0.0000291 - 0.0000194 i
23	0.5437 + 1.8375 i	6.59e-6 + 4.29e-6 i
24	0.5437 - 1.8375 i	6.59e-6 - 4.29e-6 i

  Top of the page    

Table 20. Singularities with their weights for the quadratic approximant [12, 12, 12] The most stable singularity is highlighted.
No.	zc	c	Location in the complex plane
1	-0.2501 + 0.703 i	0
2	-0.2501 - 0.703 i	0
3	-0.2485 + 0.7052 i	-1.e-10 i
4	-0.2485 - 0.7052 i	1.e-10 i
5	-0.477 + 0.6942 i	3.07e-10 i
6	-0.477 - 0.6942 i	-3.07e-10 i
7	-0.501 + 0.7178 i	3.68e-10
8	-0.501 - 0.7178 i	3.68e-10
9	-0.8571 + 0.1924 i	3.15e-10
10	-0.8571 - 0.1924 i	3.15e-10
11	-0.8606 + 0.2389 i	-3.62e-10 i
12	-0.8606 - 0.2389 i	3.62e-10 i
13	-0.0337 + 0.9375 i	2.39e-9 + 1.83e-9 i
14	-0.0337 - 0.9375 i	2.39e-9 - 1.83e-9 i
15	-0.0256 + 0.9846 i	3.2e-9 - 2.65e-9 i
16	-0.0256 - 0.9846 i	3.2e-9 + 2.65e-9 i
17	1.3404	0.00083
18	1.2544 + 0.474 i	0.0000498 + 0.00011 i
19	1.2544 - 0.474 i	0.0000498 - 0.00011 i
20	-1.4907 + 0.3006 i	9.11e-9 - 3.21e-8 i
21	-1.4907 - 0.3006 i	9.11e-9 + 3.21e-8 i
22	0.603 + 1.4707 i	1.66e-6 + 8.68e-7 i
23	0.603 - 1.4707 i	1.66e-6 - 8.68e-7 i
24	3.9474	0.102 i

  Top of the page    

Plot of singularities

List of examples

Mathematica programs

Work in UMassD

Unpublished reports

---

Designed by A. Sergeev.