Operational Calculus in Two Variables and its Applications by Unknown

Author:Unknown
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2017-11-12T05:00:00+00:00

etc. We have assumed that the function f(x, y) is differentiable in the entire region of definition and that the image functions of the derivatives exist. We may generalize these last two formulæ:

where r m, s n (r, s, m, n positive integers). In addition

with m r, n s(r, s, m, n positive integers). These formulæ are often applied in the solution of partial differential equations.

The Multiplication Rule. If F1 (p, q) f1(x, y) and F2(p, q) f2(x, y), we have the following operational relation (see Theorem 12 above), which is very useful in applications:

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