Coefficients of the powerseries, which approximates the function S(x,1)
here:	values of the coefficients a[k]				S(x,1) = -sum(a[k])
domain:	1	<= x <=	3
-1	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
	1	1.0625	1.125	1.1875	1.25	1.3125	1.375	1.4375	1.5	1.5625	1.625	1.6875	1.75	1.8125	1.875	1.9375	2	2.0625	2.125	2.1875	2.25	2.3125	2.375	2.4375	2.5	2.5625	2.625	2.6875	2.75	2.8125	2.875	2.9375
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	-0.5	-0.47142032	-0.44731400	-0.42667568	-0.40878276	-0.39310225	-0.37923212	-0.36686329	-0.35575412	-0.34571282	-0.33658524	-0.32824593	-0.32059178	-0.31353720	-0.30701053	-0.30095128	-0.29530805	-0.29003686	-0.28509981	-0.28046410	-0.27610120	-0.27198611	-0.26809688	-0.26441415	-0.26092074	-0.25760139	-0.25444245	-0.25143173	-0.24855825	-0.24581213	-0.24318443	-0.24066707
3	0	0.00076184	0.00238615	0.00422145	0.00592745	0.00734901	0.00843589	0.00919356	0.00965401	0.00985940	0.00985315	0.00967571	0.00936266	0.00894430	0.00844586	0.00788801	0.00728752	0.00665786	0.00600976	0.00535174	0.00469046	0.00403114	0.00337781	0.00273355	0.00210067	0.00148087	0.00087537	0.00028502	-0.00028966	-0.00084838	-0.00139104	-0.00191767
4	0	0.00001404	0.00007306	0.00014980	0.00019722	0.00018555	0.00011188	-0.00000643	-0.00014311	-0.00027229	-0.00037381	-0.00043487	-0.00044949	-0.00041700	-0.00034034	-0.00022462	-0.00007594	0.00009936	0.00029517	0.00050595	0.00072680	0.00095353	0.00118264	0.00141126	0.00163707	0.00185824	0.00207336	0.00228137	0.00248149	0.00267320	0.00285615	0.00303017
5	0	0.00000019	0.00000151	0.00000263	0.00000029	-0.00000469	-0.00000439	0.00001263	0.00005453	0.00012188	0.00020789	0.00030168	0.00039188	0.00046921	0.00052759	0.00056408	0.00057837	0.00057199	0.00054760	0.00050843	0.00045782	0.00039900	0.00033487	0.00026799	0.00020050	0.00013415	0.00007032	0.00001009	-0.00004576	-0.00009667	-0.00014228	-0.00018238
6	0	2.01048E-09	0.00000002	-4.95965E-09	0.00000007	0.00000172	0.00000782	0.00002009	0.00003589	0.00004890	0.00005308	0.00004628	0.00003092	0.00001229	-0.00000370	-0.00001216	-0.00001006	0.00000380	0.00002903	0.00006423	0.00010733	0.00015606	0.00020816	0.00026154	0.00031442	0.00036533	0.00041310	0.00045689	0.00049610	0.00053038	0.00055954	0.00058357
7	0	1.64532E-11	8.00130E-11	2.62464E-09	0.00000008	0.00000060	0.00000199	0.00000367	0.00000385	0.00000175	-0.00000023	0.00000214	0.00001185	0.00002874	0.00005000	0.00007162	0.00008986	0.00010214	0.00010728	0.00010532	0.00009723	0.00008449	0.00006881	0.00005187	0.00003516	0.00001995	0.00000718	-0.00000244	-0.00000851	-0.00001081	-0.00000931	-0.00000412
8	0	9.72376E-14	9.76135E-13	6.94071E-10	0.00000001	0.00000009	0.00000024	0.00000019	0.00000000	0.00000104	0.00000483	0.00001061	0.00001552	0.00001685	0.00001400	0.00000849	0.00000292	-0.00000012	0.00000109	0.00000723	0.00001802	0.00003247	0.00004927	0.00006700	0.00008433	0.00010018	0.00011373	0.00012443	0.00013201	0.00013640	0.00013770	0.00013616
9	0	2.30047E-16	3.42028E-13	7.58681E-11	1.65455E-09	0.00000001	0.00000001	0.00000001	0.00000033	0.00000141	0.00000246	0.00000213	0.00000066	0.00000005	0.00000226	0.00000771	0.00001516	0.00002259	0.00002810	0.00003053	0.00002962	0.00002585	0.00002020	0.00001381	0.00000781	0.00000311	0.00000040	0.00000005	0.00000222	0.00000683	0.00001365	0.00002234
10	0	-3.84341E-18	2.73169E-14	6.17122E-12	1.49008E-10	6.10912E-10	-3.45278E-10	0.00000003	0.00000022	0.00000036	0.00000010	0.00000010	0.00000152	0.00000410	0.00000622	0.00000648	0.00000474	0.00000213	0.00000022	0.00000028	0.00000289	0.00000786	0.00001449	0.00002179	0.00002877	0.00003462	0.00003877	0.00004093	0.00004107	0.00003936	0.00003611	0.00003172
11	0	-7.43387E-20	1.50277E-15	4.30913E-13	1.10010E-11	1.74422E-12	6.20849E-10	0.00000002	0.00000005	0.00000000	0.00000014	0.00000084	0.00000141	0.00000103	0.00000014	0.00000008	0.00000171	0.00000475	0.00000809	0.00001048	0.00001115	0.00001000	0.00000752	0.00000451	0.00000181	0.00000014	-0.00000004	0.00000144	0.00000452	0.00000893	0.00001431	0.00002022
12	0	-7.36455E-22	7.00476E-17	2.71521E-14	6.12091E-13	-3.77699E-12	4.27963E-10	0.00000001	0.00000000	0.00000003	0.00000023	0.00000027	0.00000000	0.00000016	0.00000124	0.00000254	0.00000300	0.00000225	0.00000087	-0.00000010	0.00000017	0.00000194	0.00000491	0.00000840	0.00001165	0.00001404	0.00001518	0.00001497	0.00001355	0.00001125	0.00000845	0.00000557
13	0	-1.81933E-24	2.97515E-18	1.56391E-15	1.33403E-14	4.07841E-13	1.51858E-10	7.66643E-10	1.91795E-10	0.00000004	0.00000005	-0.00000002	0.00000025	0.00000073	0.00000072	0.00000017	-0.00000009	0.00000062	0.00000218	0.00000383	0.00000474	0.00000452	0.00000332	0.00000168	0.00000029	-0.00000032	0.00000017	0.00000177	0.00000428	0.00000735	0.00001058	0.00001356
14	0	1.26307E-25	1.18691E-19	8.14151E-17	-2.47105E-15	4.15258E-13	3.85326E-11	-2.87258E-11	2.78980E-09	0.00000001	-0.00000001	0.00000010	0.00000022	0.00000005	-0.00000001	0.00000051	0.00000126	0.00000150	0.00000097	0.00000016	-0.00000020	0.00000036	0.00000180	0.00000366	0.00000535	0.00000637	0.00000647	0.00000570	0.00000429	0.00000261	0.00000105	-0.00000006
15	0	4.19229E-27	4.50856E-21	3.65674E-18	-4.58827E-16	1.36518E-13	7.30181E-12	-2.81824E-11	1.93729E-09	-8.74429E-10	0.00000002	0.00000006	-0.00000002	0.00000009	0.00000041	0.00000043	0.00000007	-0.00000009	0.00000041	0.00000136	0.00000215	0.00000226	0.00000166	0.00000069	-0.00000011	-0.00000030	0.00000031	0.00000164	0.00000340	0.00000523	0.00000677	0.00000778
16	0	9.55476E-29	1.64049E-22	1.20066E-19	-4.50405E-17	3.27092E-14	8.78729E-13	1.45893E-11	5.46560E-10	4.95171E-10	0.00000002	-0.00000001	0.00000005	0.00000015	0.00000003	-0.00000003	0.00000031	0.00000075	0.00000076	0.00000031	-0.00000013	-0.00000005	0.00000068	0.00000175	0.00000270	0.00000312	0.00000289	0.00000210	0.00000106	0.00000013	-0.00000041	-0.00000036
17	0	1.87956E-30	5.72717E-24	7.10635E-24	-1.90275E-18	6.54996E-15	-2.52340E-14	1.84727E-11	-2.32289E-11	2.35033E-09	0.00000000	0.00000001	0.00000005	-0.00000002	0.00000006	0.00000027	0.00000023	-0.00000003	-0.00000003	0.00000041	0.00000099	0.00000121	0.00000091	0.00000030	-0.00000019	-0.00000020	0.00000036	0.00000136	0.00000248	0.00000339	0.00000387	0.00000380
18	0	3.40519E-32	1.91434E-25	-4.81685E-22	3.33521E-19	1.14527E-15	-5.02830E-14	9.86679E-12	-4.63839E-11	1.17422E-09	0.00000000	0.00000002	-0.00000001	0.00000004	0.00000010	-0.00000001	-0.00000001	0.00000026	0.00000047	0.00000032	-0.00000003	-0.00000013	0.00000024	0.00000090	0.00000146	0.00000162	0.00000129	0.00000066	0.00000001	-0.00000035	-0.00000026	0.00000031
19	0	5.84166E-34	6.08448E-27	-5.90940E-23	1.11389E-19	1.75792E-16	-1.57546E-14	3.37130E-12	2.83708E-11	-6.26575E-11	0.00000000	0.00000000	0.00000001	0.00000003	-0.00000002	0.00000006	0.00000019	0.00000008	-0.00000007	0.00000006	0.00000044	0.00000068	0.00000054	0.00000013	-0.00000018	-0.00000012	0.00000035	0.00000106	0.00000170	0.00000202	0.00000192	0.00000145
20	0	9.62799E-36	1.81113E-28	-5.31011E-24	2.12508E-20	2.28859E-17	-2.37116E-15	6.29643E-13	4.45789E-11	-1.14050E-10	1.38351E-09	8.83579E-10	0.00000001	-0.00000001	0.00000005	0.00000006	-0.00000003	0.00000004	0.00000024	0.00000026	0.00000004	-0.00000012	0.00000006	0.00000048	0.00000084	0.00000087	0.00000055	0.00000009	-0.00000024	-0.00000024	0.00000014	0.00000079
21	0	1.53754E-37	4.88009E-30	-4.13212E-25	3.32267E-21	2.18298E-18	3.66947E-16	-8.62805E-14	2.22345E-11	1.73632E-10	-5.03645E-10	4.73394E-09	0.00000000	0.00000002	0.00000001	-0.00000002	0.00000008	0.00000011	-0.00000002	-0.00000004	0.00000018	0.00000039	0.00000033	0.00000006	-0.00000015	-0.00000007	0.00000032	0.00000079	0.00000109	0.00000108	0.00000076	0.00000028
22	0	2.39180E-39	1.08484E-31	-2.92229E-26	4.64274E-22	2.17077E-20	4.38063E-16	-1.25046E-13	2.23550E-12	1.67360E-10	1.77662E-10	1.90037E-10	0.00000000	0.00000001	0.00000000	0.00000005	0.00000001	-0.00000003	0.00000009	0.00000018	0.00000007	-0.00000008	-0.00000001	0.00000027	0.00000050	0.00000048	0.00000020	-0.00000011	-0.00000022	-0.00000003	0.00000040	0.00000089
23	0	3.63714E-41	1.25501E-33	-1.90612E-27	6.00031E-23	-6.00883E-20	2.07485E-16	-5.02084E-14	-3.55613E-12	1.38678E-11	6.26735E-10	-5.97758E-10	0.00000000	0.00000000	0.00000002	-0.00000001	0.00000001	0.00000008	0.00000003	-0.00000005	0.00000005	0.00000022	0.00000022	0.00000002	-0.00000012	-0.00000003	0.00000027	0.00000057	0.00000066	0.00000048	0.00000014	-0.00000016
24	0	5.41942E-43	-5.63787E-35	-1.14186E-28	7.28700E-24	-2.07856E-20	7.42490E-17	-4.38756E-15	-1.54434E-12	-3.65109E-11	7.10159E-11	1.38220E-09	0.00000000	0.00000001	0.00000000	0.00000001	0.00000003	-0.00000002	0.00000001	0.00000011	0.00000007	-0.00000005	-0.00000003	0.00000016	0.00000032	0.00000026	0.00000004	-0.00000015	-0.00000012	0.00000013	0.00000048	0.00000074
25	0	7.92434E-45	-5.83374E-36	-6.10876E-30	8.36784E-25	-5.11279E-21	2.22286E-17	8.74264E-15	8.82435E-13	4.26008E-12	-1.55636E-10	4.07610E-10	0.00000000	0.00000000	0.00000000	0.00000001	-0.00000001	0.00000003	0.00000004	-0.00000003	0.00000000	0.00000012	0.00000015	0.00000001	-0.00000010	-0.00000001	0.00000022	0.00000039	0.00000035	0.00000014	-0.00000011	-0.00000021
26	0	1.13807E-46	-3.49896E-37	-2.66748E-31	9.07759E-26	-1.07311E-21	5.63978E-18	7.71897E-15	1.31651E-12	2.71638E-11	9.09994E-11	-4.49770E-10	0.00000000	0.00000000	0.00000001	-0.00000001	0.00000002	0.00000000	-0.00000002	0.00000006	0.00000007	-0.00000003	-0.00000004	0.00000009	0.00000020	0.00000014	-0.00000003	-0.00000013	-0.00000003	0.00000021	0.00000043	0.00000047
27	0	1.60581E-48	-1.76611E-38	-5.95716E-33	9.21652E-27	-2.01941E-22	1.14395E-18	3.98665E-15	5.90811E-13	9.59396E-12	1.26712E-10	3.19021E-10	0.00000000	0.00000000	0.00000000	0.00000001	-0.00000001	0.00000000	0.00000004	-0.00000001	-0.00000002	0.00000007	0.00000010	0.00000000	-0.00000008	0.00000001	0.00000018	0.00000025	0.00000016	-0.00000004	-0.00000016	-0.00000010
28	0	2.22534E-50	-8.16785E-40	5.37739E-34	8.54600E-28	-3.44736E-23	1.33486E-19	1.37008E-15	-7.18672E-14	-7.50847E-12	-3.18163E-11	3.00669E-10	0.00000000	0.00000000	0.00000000	0.00000000	0.00000001	0.00000002	-0.00000002	0.00000002	0.00000005	-0.00000001	-0.00000004	0.00000006	0.00000013	0.00000007	-0.00000006	-0.00000009	0.00000004	0.00000022	0.00000030	0.00000022
29	0	3.02573E-52	-3.57969E-41	1.06621E-34	6.78406E-29	-5.26872E-24	-2.78383E-20	1.79560E-16	-2.46176E-13	-4.67039E-12	-4.11021E-11	-2.06380E-10	6.23313E-10	3.71097E-10	-2.36607E-10	0.00000000	0.00000001	-0.00000001	0.00000002	0.00000001	-0.00000003	0.00000003	0.00000007	0.00000000	-0.00000006	0.00000001	0.00000014	0.00000015	0.00000004	-0.00000010	-0.00000011	0.00000003
30	0	4.02862E-54	-1.51211E-42	1.22909E-35	3.60124E-30	-6.82302E-25	-2.77596E-20	-1.67611E-16	-1.18627E-13	3.48352E-12	3.69689E-11	5.92131E-12	-5.31255E-10	1.31431E-09	-9.05707E-10	0.00000000	0.00000000	0.00000001	-0.00000001	0.00000000	0.00000004	0.00000000	-0.00000003	0.00000003	0.00000009	0.00000003	-0.00000006	-0.00000005	0.00000007	0.00000019	0.00000017	0.00000003
31	0	5.23544E-56	-6.21676E-44	1.18854E-36	-1.38299E-31	-6.01775E-26	-1.32403E-20	-1.75327E-16	2.56628E-14	3.59789E-12	2.37356E-11	1.66326E-10	2.13899E-10	-1.01962E-09	2.51136E-09	0.00000000	0.00000001	-0.00000001	0.00000001	0.00000001	-0.00000002	0.00000001	0.00000005	0.00000000	-0.00000005	0.00000002	0.00000010	0.00000008	-0.00000003	-0.00000009	-0.00000003	0.00000011
32	0	6.60496E-58	-2.50294E-45	1.04872E-37	-8.60272E-32	2.44856E-27	-5.03277E-21	-1.03344E-16	6.62238E-14	-8.06584E-13	-2.21880E-11	-6.47255E-11	2.74633E-10	5.08225E-10	-1.56764E-09	0.00000000	0.00000000	0.00000001	0.00000000	-0.00000001	0.00000002	0.00000000	-0.00000003	0.00000002	0.00000006	0.00000001	-0.00000006	-0.00000002	0.00000009	0.00000013	0.00000006	-0.00000006
S(x)=	0.500000	0.470644	0.444853	0.422302	0.402658	0.385570	0.370679	0.357640	0.346148	0.335950	0.326837	0.318641	0.311224	0.304476	0.298306	0.292638	0.287409	0.282567	0.278067	0.273873	0.269951	0.266274	0.262818	0.259562	0.256488	0.253579	0.250821	0.248203	0.245712	0.243339	0.241075	0.238912