Schedule of Classification 



2920 Irrationality and transcen- 

 dence of particular num- 

 bers, such as e and TT. 

 (See also 6810.) ... ... 232 



e 232-233 



TT... 233 



3190 General 



ANALYSIS. 



233 



Foundations of Analysis. 



3200 General 234 



3210 Theory of functions of real 



variables 235 



3220 Infinite series ; infinite pro- 

 ducts and other infinite 

 processes. (See also 5610, 



5620.) 238 



Infinite series ... 238-252 



Binomial theorem 238-239 



Convergence ... 239-241 



Expansion ... 242-244 



Power series ... 245-246 



Summation ... 248-250 



Trigonometric series 250-251 



Infinite products ... 252-253 



Other infinite processes ... 253 



3230 Principles and elements of 



the differential calculus 253 

 3240 Taylor's series. Maxima and 

 minima ; other analytical 

 applications of the differen- 

 tial calculus 259 



Lagrange's series ... 261 



Other series 261 



Maxima and Minima 262-263 



Maxima 264 



Minima 264 



Taylor's series ... 265-266 



3250 Principles and elements of 

 the integral calculus. Ap- 

 proximate integration. 

 Mechanical quadrature 267 



Integral calculus 268 



Integration ... 270-272 



3260 Definite integrals (simple) ... 274 



Evaluation ... 277-278 



Transformation ... 280 



3270 Multiple integrals 283 



Double integrals 284-285 



3280 Calculus of variations ... 286 



Theory of Functions of Complex 

 Variables. 



3600 General 289 



3610 Uniform functions of one 



variable 292 



3620 Multiform functions of one 

 variable ; Rieinann sur- 

 faces. (See also 4060, 



6420, 8075.) 296 



Biemann surfaces 296-297 



3630 Expansions in series of func- 

 tions, other than powers of 

 the variable ... ... 297 



3640 Functions of several variables 298 



Algebraic Functions and their Integrals. 



4000 General 299 



4010 Algebraic functions of one 



variable 301 



4020 Algebraic functions of several 



variables 302 



4030 Logarithmic, circular, ex- 

 ponential functions ... 303 

 Circular functions 303-305 



Expansion ... 303-304 



Logarithmic and exponen- 

 tial functions 305-311 

 Logarithmic tables ... 308 

 4040 General properties of elliptic 

 functions and single theta 

 functions ; addition-theo- 

 rem. (See also 8050, 8060.) 311 



Addition 311 



Addition-theorem 311-312 

 Doubly periodic func- 

 tions 312-313 



Elliptic functions... 313-319 



Elliptic integrals 319-321 



Theta functions ... 323-324 



4050 Multiplication,division,trans- 

 formation of elliptic func- 

 tions; modular functions. 



(See also 4440.) 325 



Division 325 



Modular equations ... 326 

 Modular functions . . . 326 



Multiplication ... ... 327 



Transformation ... 327-329 



4060 Abelian integrals. (See also 



8050, 8060.) 329 



A belian functions 329-331 



Abelian integrals . . . 331-333 



Abel's theorem ... 333-334 



4070 Periodic functions of several 

 variables ; general theta 

 functions 335 



Other Special Functions. 



4400 General 338 



4410 Eulerian functions 339 



Eulerian integrals ... 340 



Gamma functions 340-342 



4420 Legendre's functions; Bessel's 



functions ; hypergeo- 



metric functions ... 342 



Bessel's functions 343-344 



Cylindrical functions ... 344 



Hypergeometric functions 344-345 



Hyper geometric series 345-346 



Legendre's functions 346-347 



Legendre's polynomials 347 



Spherical harmonics 347-348 



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