Issue 45

O. Reut et alii, Frattura ed Integrità Strutturale, 45 (2018) 183-190; DOI: 10.3221/IGF-ESIS.45.16 186       0 , , , , n i in n x q K x e d dx x x q                                                          Finally, we derive the expression for the function’s transformation n k   through the transformations of its jump and the jump of its normal derivative             2 2 sin cos cos 1/ 2 n n n k n k n k P P t k                  (10) D ERIVING THE FINAL FORMULA he inverse Legendre’s transformation is applied to (10)     cos n n kn k n k k n P            (11) where       1/ 2 ! ! kn k k n k n      Then the inverse Kantorovich-Lebedev transformation is applied to the obtained expression       0 , i n n K x x sh d q x                   Bearing in mind that the expressions for the transformations of the wave potential jumps and its normal derivative have the following form       0 , , n n i n n q K d q                                                       in the Fourier’s transformation domain, the wave potential has the following form               2 2 0 0 , sin cos 1/ 2 cos , cos , n i i n kn k k n n n k n k n sh K x K x P q x k P P d d q q                                                                    The integral in the last formula is known [ 2.16.52(11), 20] T