2890 Application of other transcendental functions to 



arithmetic. 

 2900 Distribution of prime numbers. 

 2910 Special numerical functions. 

 2920 Irrationality and transcendence of particular numbers, 



such as e and ir. 



(For applications of arithmetic methods to 

 algebraic functions see 4010.) 



ANALYSIS. 



Foundations of Analysis. 



3200 General. 



3210 Theory of functions of real variables. 



3220 Series ; infinite products and other infinite processes. 



{See also 5610, 5620.) 

 3230 Principles and elements of the differential calculus. 

 3240 Taylor's series, maxima and minima ; other analytical 



applications of the differential calculus. 

 3250 Principles and elements of the integral calculus. 

 3260 Definite integrals (simple). 

 3270 Multiple integrals. 

 3280 Calculus of variations. 



Theory of Functions of Complex Variables. 



3600 General 



3610 Uniform functions of one variable. 



3620 Multiform functions of one variable ; Riemann 



surfaces. 

 3630 Expansions in series of functions, other than powers 



of the variable. 

 3640 Functions of several variables. 



Algebraic Functions and their Integrals. 



4000 General. 



'1010 Algebraic functions of one variable. 



4020 Algebraic functions of several variables. 



4030 Logaiithmic, circulnr, exponential functions. 



4040 General properties of elliptic functions and single theta 



functions; addition-theorem. ((S'e^? also 8050,8060.) 

 4050 Multiplication, division, transformation of elliptic 



functions ; modular functions. {See also 4440.) 

 4060 Abelian integrals. {See also 8050, 8060.) 

 4070" Periodic functions of several variables ; general theU* 



functions. 



Other Special Functions. 



4400 General. 



4410 Eulerian functions. 



