93 - 94

S.B. Karavashkin and O.N. Karavashkina

This system will have the following solution:

The solutions (50) take place on the bands

94

Passing now to the initial independent variable, we yield the solution of differential equation (43) in the intervals n related to (51):

However limited the band (51) is (which we can much broaden with recurrent relationships), we see that, so to say, the field principle to represent the function of complex variable offers to use more completely the advantages of the theory of complex variables to solve the physical and mathematical problems, in particular - to seek the solutions of non-trivial differential equations.

1. Lavrentiev, M.A. and Shabat, B.V. The methods of theory of complex variable. Nauka, Moscow, 1973, 736 pp. (Russian)

2. Bitsadze, A.V. Foundations of the theory of analytical functions of complex variable. Nauka, Moscow, 1969, 239 pp. (Russian)

3. Gray, A. and Mathews, G.B. Bessel functions and their applications to physics and mechanics. Inosstrannaya literatura, Moscow, 1953, 371 pp. (russian; from edition: Gray, A. and Mathews, G.B. A treatise on Bessel functions and their applications to physics. English edition of 1931)

1985