Table 3.

t_max and g(t_max) as a function of β, where g(t) is the inverse Laplace transform of ${\mathrm{e}}^{-s\beta }$

β	tmax	g(tmax)
0.15	0.00000190503	450.9129
0.16	0.00000630739	209.22449
0.17	0.0000177337	108.862395
0.18	0.0000436172	62.162073
0.19	0.0000960414	38.311543
0.20	0.000192795	25.155645
0.21	0.000357987	17.416529
0.22	0.000622088	12.610041
0.23	0.00102137	9.484013
0.24	0.00159686	7.369062
0.25	0.00239285	5.888686
0.26	0.00345532	4.821523
0.27	0.00483018	4.032270
0.28	0.00656175	3.435337
0.29	0.00869134	2.974907
0.30	0.0112561	2.613581
0.31	0.0142884	2.325679
0.32	0.0178147	2.093179
0.33	0.0218560	1.903181
0.34	0.0264274	1.746284
0.35	0.0315381	1.615524
0.36	0.0371920	1.505665
0.37	0.0433880	1.412716
0.38	0.0501201	1.333598
0.39	0.0573788	1.265907
0.40	0.0651506	1.207748
0.41	0.0734193	1.157611
0.42	0.0821662	1.114283
0.43	0.0913707	1.076782
0.44	0.101011	1.044308
0.45	0.111063	1.016202
0.46	0.121503	0.991922
0.47	0.132308	0.971016
0.48	0.143453	0.953108
0.49	0.154914	0.937885
0.50	0.166667	0.925082
0.51	0.178689	0.914477
0.52	0.190959	0.905885
0.53	0.203454	0.899150
0.54	0.216155	0.894139
0.55	0.229042	0.890746
0.56	0.242097	0.888881
0.57	0.255304	0.888472
0.58	0.268646	0.889461
0.59	0.282109	0.891806
0.60	0.295680	0.895475
0.61	0.309346	0.900451
0.62	0.323098	0.906726
0.63	0.336924	0.914305
0.64	0.350818	0.923202
0.65	0.364772	0.933445
0.66	0.378780	0.945070
0.67	0.392837	0.958129
0.68	0.406941	0.972686
0.69	0.421088	0.988819
0.70	0.435279	1.006623
0.71	0.449512	1.026212
0.72	0.463791	1.047719
0.73	0.478118	1.071303
0.74	0.492496	1.097151
0.75	0.506933	1.125483
0.76	0.521435	1.156560
0.77	0.536011	1.190689
0.78	0.550671	1.228239
0.79	0.565430	1.269648
0.80	0.580300	1.315445
0.81	0.595300	1.366273
0.82	0.610450	1.422918
0.83	0.625773	1.486349
0.84	0.641295	1.557781
0.85	0.657048	1.638750
0.86	0.673068	1.731228
0.87	0.689397	1.837792
0.88	0.706087	1.961869
0.89	0.723197	2.108126
0.90	0.740799	2.283081
0.91	0.758982	2.496129
0.92	0.777856	2.761327
0.93	0.797561	3.100708
0.94	0.818279	3.550899
0.95	0.840258	4.177648
0.96	0.863851	5.112078
0.97	0.889596	6.659241
0.98	0.918411	9.731437
0.990	0.9522311	18.874343
0.995	0.9725934	37.055102
0.997	0.9819976	61.229747
0.998	0.9871752	91.409296
0.999	0.9928860	181.858807
1.000	1.0000000	INFINITY
1/3	0.0233204	1.847590
2/3	0.388146	0.953613
0.56787475	0.25248543	0.888440006391162 =lowest value of g(tmax)