Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

For the first case, for points -5, -4, -2, 1, 3, 5 the initial data obtained by formula (17) will have the following form. As a result of calculating the series rjad_cos (x), we get the values of cos (x). _1_cos ( ) ≔ 2 0 + 2 1 + 2 2 ∙ 2 + 2 3 ∙ 3 + 2 4 ∙ 4 + 2 5 ∙ 5 (19) The graphs of these two functions cos (x) and rjad_1_cos(x) and some values of these graphs are shown in Figure 3. Figure 3: Values of the functions- rjad_1_cos (x) and cos (x) _1_cos (−5) = 0.284 _1_cos (−4) = −0.654 cos(−5) = 0.284 cos(−4) = −0.284 _1_cos (−2) = −0.416 _1_cos (−1) = 0.54 cos(−2) = −0.416 cos(−1) = 0.54 _1_cos (3) = −0.99 _1_cos (5) = 0.284 cos(3) = −0.99 cos(5) = 0.284 b2 0.615 0.207 0.257 − 0.036 − 9.731 10 3 − × 1.117 10 3 − ×                   = 5 − 0 5 2 − 1 − 1 2 rjad_1_cos x( ) cos x( ) 2 − 3 x A2 1 1 1 1 1 1 5 − 4 − 2 − 1 3 5 25 16 4 1 9 25 125 − 64 − 8 − 1 27 125 625 256 16 1 81 625 3125 − 1024 − 32 − 1 243 3125                 := B2 cos 5 − ( ) cos 4 − ( ) cos 2 − ( ) cos 1( ) cos 3( ) cos 5( )                 := b2 A2 1 − B2 ⋅ := Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 14 Year 2023 © 2023 Global Journals ( ) I Application of Differentialintegral Functions