The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet
The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet
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In our eReader you can find the full English version of the book. Read The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet
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16) of (2. 1) can be obtained more easily without the introduction of a Hilbert-Riemann problem if we use the following technique which may be new. Introduce (2. 17) F(w) = (j} 4>(z), QZ Z - W and hence (2. 13) f"*"(0 = 7ri(0 + ^ -^ dz .
If (^(z) is to satisfy (2. 1) v/e must have (2. 19) F^iO = [7ri + h(O]0(i;) + f(?) or (2. 20) HI) - Sferrf^ • The substitution of this in (2. 1) gives *«' ^ «^> In accordance with our assumption the zeros of h(l, ) + ni lie in a domain D- which, with its counte...rclockwise orientated boundary C, , is contained in D . In the integral involving F (z) in (2. 21) let C be contracted into C . Since F(v/) is analytic in D, equation (2. 21) gives h(^)M?) + f(0 = Pr^- I „. , J^L^^, . + / ^^'■^^'' h(U + 7ri r [h{z) + ^ij(z-U f [h(z) + 7ri](z - ^ {'•, :- 10 or, using (2. 19), r [h(z) + 7ri, (z - i) c ^1 from which we find ■ty\ - ^(g>^('^) 1 I f(z) dz '*'^"' " h^O + TT^ ' [h(i>)-7ri: J [h(z) + ^ij(z - O (2. 22) [h(U-7ri] f ^ - ^ F(z) dz [h(U - TTi] r [h(z) + 7rij(z - U ^1 + + If h(z) + TTi is analytic in D + C with simple zeros in E at a, k = 1, 2, .
What to read after The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
16) of (2. 1) can be obtained more easily without the introduction of a Hilbert-Riemann problem if we use the following technique which may be new. Introduce (2. 17) F(w) = (j} 4>(z), QZ Z - W and hence (2. 13) f"*"(0 = 7ri(0 + ^ -^ dz .
If (^(z) is to satisfy (2. 1) v/e must have (2. 19) F^iO = [7ri + h(O]0(i;) + f(?) or (2. 20) HI) - Sferrf^ • The substitution of this in (2. 1) gives *«' ^ «^> In accordance with our assumption the zeros of h(l, ) + ni lie in a domain D- which, with its counte...rclockwise orientated boundary C, , is contained in D . In the integral involving F (z) in (2. 21) let C be contracted into C . Since F(v/) is analytic in D, equation (2. 21) gives h(^)M?) + f(0 = Pr^- I „. , J^L^^, . + / ^^'■^^'' h(U + 7ri r [h{z) + ^ij(z-U f [h(z) + 7ri](z - ^ {'•, :- 10 or, using (2. 19), r [h(z) + 7ri, (z - i) c ^1 from which we find ■ty\ - ^(g>^('^) 1 I f(z) dz '*'^"' " h^O + TT^ ' [h(i>)-7ri: J [h(z) + ^ij(z - O (2. 22) [h(U-7ri] f ^ - ^ F(z) dz [h(U - TTi] r [h(z) + 7rij(z - U ^1 + + If h(z) + TTi is analytic in D + C with simple zeros in E at a, k = 1, 2, .
What to read after The Solution of Certain Integral Equations With Kernels K Z Zeta Z Zet?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
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