Bessel Equation in the Semiunbounded Interval : Solving in the Neighbourhood of an Irregular Singular Point

Table 4

Comparisons of the zero points of the Bessel function in Example 1 between the asymptotic formula and the corrected Fourier series in this study.

7	21.6770	21.68	20.7345	20.73
8	24.8186	24.82	23.8761	23.87
9	27.9602	27.96	27.0177	27.01
10	31.1018	31.10	30.1593	30.16
11	34.2433	34.24	33.3009	33.30
12	37.3849	37.38	36.4425	36.44
13	40.5265	40.52	39.5841	39.58
14	43.6681	43.67	42.7257	42.72
15	46.8091	46.81	45.8672	45.86
16	49.9513	49.95	49.0088	49.00
17	53.0929	53.09	52.1504	52.15
18	56.2345	56.23	55.2920	55.29
19	59.3761	59.37	58.4336	58.43
20	62.5177	62.51	61.5752	61.57

Relative errors:
, 
.