5 9 4 D O C . 3 8 5 Q U A N T U M T H E O R Y O F I D E A L G A S I I [23]In the manuscript, Einstein had written “(Bürmann Lagrange),” then deleted “Bürmann” and indicated a footnote after “Satz”: “Vgl. Hurwitz–Courant. Funktionentheorie S. 128.,” which he then deleted. The reference is to Hurwitz 1922, which on p. 128 cites a theorem about the inversion of power series according to which, under certain conditions, a regular function f(z) can be expanded as , with given by , where and , such that f(z) is given in powers of . In the book, the expan- sion is called “Bürmann-Lagrangesche Reihe.” [24]This implicitly corrects an earlier mistake in Einstein 1924o (Doc. 283), eq. (22a) (see its note 14). f z) ( f(0) k1w k2w2 knwn + + + + + = kn kn 1 n! ----Dz - n 1 f'(z) z P(z)¹ -----------· © § n z 0 = = Dz n dn dzn ------- -= w P(z) = P(z)
Previous Page Next Page