93 - 94

S.B. Karavashkin

The solution of this system is

This solution is true in the range

94

Transiting to the initial independent variable, we obtain the solution of differential equation (43) in the range of n, corresponding to (51):

Though the range (51) is so limited (but can be well widen by the recurrence relations), we see that the "field" principle to present the function of complex variable enables us using better the merits of the theory of functions of complex variables to solve the physical and mathematical problems, particularly for seeking 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