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)