1245 
ore, around which a mixture of ore and prisms of gold-coloured 
aegirine-augite columns is ‘formed. 
The metamorphoses described above by which gold-coloured pyroxe- 
nes with the optical properties of aegirine-augites are formed, appear 
to be connected with pneumatolytie processes in magmas rich in alkali. 
Finally it may be mentioned here, that to the South of the road 
Panarukan Besuki, quite near to mile-post 13, a loose piece of a 
leucitite was found with phenocrysts of leucites as large as 4 m.m., 
which certainly had come down from the northern slope of the Ringgit 
and consequently may be expected there in greater quantities; hitherto 
such types of rocks were not recorded from the Ringgit-mountain. 
Mathematics. — “Hupansion of a function in series of ABEL’s 
functions p‚lx)’. By Prof. W. KapPrern. 
(Communicated in-the meeting of February 22, 1913). 
1. In the Oeuvres completes of ABEL') may be found the follow- 
ing expansion : 
Xv 
1 GEE op 
——— @ "— Ss Pula)vr 
1l—v 0 
where 
; yn _n vw? nun 
pile) = 1—Cye + Co it aes + (—1) En 
a: nN: 
C5 representing the binomial coefficients. 
These polynomia form the object of the dissertation of Dr. A. A. 
NigLanp (Utrecht 1896) and have been treated afterwards by E. Le 
Roy in his memoir “Sur les séries divergentes” (Annales de Toulouse 
1899). 
In this paper I wish to examine when a given function of a real 
variable may be expanded in a series of this form 
bl Aar anne) Hee lener U 
2. In this article we collect those properties of the polynomia 
g(a) which we want for our investigation and which we take from 
NiJLAND's dissertation. 
In the first place we have the important relations 
1) Oeuvres Completes IT p. 284. 
