Forward Scattering of High Frequency Plane Waves By a Sphere
Forward Scattering of High Frequency Plane Waves By a Sphere
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Therefore h (kr) are the radial eigen- n functions, and (2, 6) is the above-mentioned alternate expansion of the solu- tion in terms of the radial eigenf unctions. The convergence properties of these two representations (2. 6) and (2, Ii) have already been mentioned in the Introduction, 3, Subtraction of the plane wave We wish to obtain a representation for the scattered wave that will exhibit the convergence properties of an expansion in terms of radial modes. -5- Since the plane wave cannot b...e split off directly fl*om (2, 6), as it «as from (2, U), it must be subtracted in some other manner. To this end, we first represent the plane wave given by (2, 5) by a contour integral. Ac- cordingly, we may write u. In the form r 3 (l(r)(2v (3. 1) "1 = ^ J r 2v+l) e ivn/2 P^(cos 9) xvn e sin vn dv where the residues reduce to the series (2, 5) when the contour is taken as shown in Fig, 2, /3 (v ♦ l/2)-plane 7 Z Figure 2 (3. 2) The lower branch of the contour may be reflected by introducing - V - 1, because then - 6 - » V +1/2= -00 (3.
What to read after Forward Scattering of High Frequency Plane Waves By a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by George Kear to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Therefore h (kr) are the radial eigen- n functions, and (2, 6) is the above-mentioned alternate expansion of the solu- tion in terms of the radial eigenf unctions. The convergence properties of these two representations (2. 6) and (2, Ii) have already been mentioned in the Introduction, 3, Subtraction of the plane wave We wish to obtain a representation for the scattered wave that will exhibit the convergence properties of an expansion in terms of radial modes. -5- Since the plane wave cannot b...e split off directly fl*om (2, 6), as it «as from (2, U), it must be subtracted in some other manner. To this end, we first represent the plane wave given by (2, 5) by a contour integral. Ac- cordingly, we may write u. In the form r 3 (l(r)(2v (3. 1) "1 = ^ J r 2v+l) e ivn/2 P^(cos 9) xvn e sin vn dv where the residues reduce to the series (2, 5) when the contour is taken as shown in Fig, 2, /3 (v ♦ l/2)-plane 7 Z Figure 2 (3. 2) The lower branch of the contour may be reflected by introducing - V - 1, because then - 6 - » V +1/2= -00 (3.
What to read after Forward Scattering of High Frequency Plane Waves By a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by George Kear to read onlineMoreLess
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