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)
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