# tailieunhanh - Handbook of mathematics for engineers and scienteists part 126

## Handbook of mathematics for engineers and scienteists part 126. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Linear Integral Equations of the Second Kind with Constant Limits of Integration 843 On applying the Mellin transform to equation and taking into account the fact that the integral with such a kernel is transformed into the product by the rule see Subsection M 1 Q t y t dt Q s y s I Jo t 7 t 7 J we obtain the following equation for the transform y s y s - Q s y s f s . The solution of this equation is given by the formula A f s i s -_ Q- On applying the Mellin inversion formula to equation we obtain the solution of the original integral equation 1 c ix f s L SQ ds 164 9 This solution can also be represented via the resolvent in the form y x f x i 1N fX f t dt Jo t v t 7 where we have used the notation N x M-1 N s N s Q . 1 - Q s under the application of this analytical method of solution the following technical difficulties can occur a in the calculation of the transform for a given kernel K x and b in the calculation of the solution for the known transform y s . To find the corresponding integrals tables of direct and inverse Mellin transforms are applied . see Sections and . In many cases the relationship between the Mellin transform and the Fourier and Laplace transforms is first used M f x s F f ex is L f ex -s L f e x s and then tables of direct and inverse Fourier transforms and Laplace transforms are applied see Sections . . Equation with the kernel K x t t3Q xt on the semiaxis. Consider the following equation on the semiaxis y x - t3Q xt y t dt f x . 0 844 Integral Equations To solve this equation we apply the Mellin transform. On multiplying equation by xs-1 and integrating with respect to x from zero to infinity we obtain i y x xs-1 dx - i y t t dt i Q xt xs-1 dx i f x xs-1 dx. Jo Jo Jo Jo Let us make the change of variables z xt. We finally obtain y s - Q s y f t s dt f s . o Taking into account the relation r y

TÀI LIỆU LIÊN QUAN
4    68    0
24    189    2
77    318    10
132    101    3
11    125    0
90    156    9
97    140    1
3    64    2
63    83    1
63    119    1
TÀI LIỆU XEM NHIỀU
8    460196    47
14    12377    36
13    9230    483
3    8200    102
14    7982    416
8    6781    2142
16    6755    397
249    5879    980
7    4675    3
17    4522    195
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
84    113    1    30-01-2023
19    109    1    30-01-2023
8    113    1    30-01-2023
204    106    0    30-01-2023
5    92    0    30-01-2023
32    123    0    30-01-2023
126    98    1    30-01-2023
7    92    0    30-01-2023
3    100    0    30-01-2023
14    71    0    30-01-2023
TÀI LIỆU HOT
8    6781    2142
112    2541    1120
249    5879    980
561    1870    574
152    2105    517
122    2639    491
13    9230    483
62    1963    481
35    2738    436
14    7982    416
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.