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

Figure 8: Values of the functions – cos(x) and _cos (x) Additionally, the application of differential integration functions in music, curves of equal loudness, for example, Fletcher-Manson curves or Robinson-Dudson curves, Figure 9, is presented. _A _SL i j , ( ) SL x i n j , 0 , ( ) ← i 0 11 .. ∈ for j 0 11 .. ∈ for := 4 4.5 5 5.5 6 1 − 0.5 − 0.5 1 cos x( ) _cos x( ) x KRG 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 20 40 63 100 160 200 250 315 400 500 630 800 3 1·10 3 1.25·10 3 1.6·10 3 2·10 3 2.5·10 3 3.15·10 3 4·10 3 5·10 3 6.3·10 3 8·10 4 1·10 1.25·10 2.996 3.689 4.143 4.605 5.075 5.298 5.521 5.753 5.991 6.215 6.446 6.685 6.908 7.131 7.378 7.601 7.824 8.055 8.294 8.517 8.748 8.987 9.21 9.433 119 105.3 98.4 92.5 87.8 85.9 84.3 82.9 81.7 80.9 80.2 79.7 80 82.5 83.7 80.6 77.9 77.1 78.3 81.6 86.8 91.4 91.7 85.4 = a __A 1 − ( ) B ⋅ := n 0 1 2 3 4 5 6 7 8 9 10 11                               := x 2.996 4.143 5.753 6.685 6.908 7.378 7.824 8.055 8.517 8.987 9.21 9.433                               := y 119 98.4 82.9 79.7 80 83.7 77.9 77.1 81.6 91.4 91.7 85.4                               := i 0 23 .. := SL x n , k , ( ) x n k − Γ n 1 + ( ) ⋅ Γ n k − 1 + ( ) := 0 2 , 7 , 11 , 12 , 14 , 16 , 17 , 19 , 21 , 22 , 23 , j 0 23 .. := k 0 := © 2023 Global Journals Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 19 Year 2023 ( ) I Application of Differentialintegral Functions