Overview

A fundamental property of permutability is expressed in the following theorem: Two functions permutable with a third are permutable with each other. A group of permutable functions is characterized by a function of the first order of which the first and second partial derivatives exist and are finite. Consequently when we consider a group of permutable functions, we shall always assume that there is known to us a function of the first order which has finite derivatives of the first and second orders and belongs to the group . This function shall be spoken of as the fundamental function of the group. When a fundamental function of the group has the canonical form, we shall speak of the group as a canonical group.

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9781098982614

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