4420 Legendre's functions ; Bessel's functions ; hyper- 

 geometric functions. 



4430 Other functions which may be defined by definite 

 integials. {See also 4860.; 



4440 Automorphic functions. (See also 1220, 4050.) 



4450 Other functions which may be defined by luiear 

 differential equations. (See also 4850.) 



4460 Other functions vvliich may be defined by functional 

 equations. (See also 6030.) 



Differential Equations. 



4800 General. 



4810 Existence-theorems for ordinary and paitial differential 

 equations. 



4820 Methods of solution and reduction of ordinary 

 differential equations. 



4830 Methods of solution and redaction of partial differen- 

 tial equations cf the first order, inclnding the 

 differential equations of theoretical dynamics. 



4840 Methods of solution and redu(;tion of partial differen- 

 tial equations of the second and higher orders. 



4850 General theory of ordinary linear equations. (See 

 also 4450.) 



4860 Integration of ordinary linear equations by definite 

 integrals. (See also 4430.) 



4870 Genei-al theory of ordinary equations, not Jiuear-, of the 

 first order. 



4880 General theory of ordinary equations, not linear, of 

 order higher than the first. 



Differential Forms and Differential Invariants. 



5200 General. 



5210 Linear differential forms ; PfaflBans. 



5220 Differential foi-ras of the second and higher orders. 

 (See also 8450.) 



5230 Transformation of differ-erjtial forms, including tan- 

 gential (or contact) transfor-mations. 



5240 Differential invar-iants. (See also 1230. 1240.) 



Analytical Methods connected With Physical Problems. 



5600 General. (See also B 2000-2100, 3220.) 



5610 Harmonic analysis ; Fourier's series. (See also 3220.) 



5620 Harmonic analysis; series othei- than Fourier's, 

 (See also 3220.) 



5630 Gener*alities on the differential e(]uations of mathe- 

 matical physics. (See also B 2020.) 



5640 Integration of the differerrtial equations of mathe- 

 matical physics 1)3' series. 



5650 Integiaticm of the differential equatiorrs of mathe- 

 matical physics by definite integrals. 



5660 Dirichlet's problem and nnalogoiis problems, affected 

 by boundary conditions. 



