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A Theorem on Rational Integral Symmetric Functions

1929
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Mathematical Notes
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An identity involving symmetric functions of n letters may in ĉ ertain class of cases be extended immediately to a greater number of letters. For example, the theorem (a + b) 2 = a 2 + *> 2 + 2ab may be written (2 a) 2 = 2a 2 + 2 2a6; and in the latter form it is true for any number of letters. Similarly with the theorem (a + b + c) 3 = a 3 + b 3 + c 3 + 3a 2 (b + c) + 36 2 (c + a) + 3c 2 (a + b) + 6a6c; (1) in the form it is true for any number of letters. The symmetric functions which occur

doi:10.1017/s1757748900001894
fatcat:xi7n65hkm5gsjd5dy6tt4lnw6a