6 



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

 geometric functions. 



4430 Other functions which may be defined by definite 

 integ-rals. (iS'es also 4860.) 



4440 Automorphic functions. {See also 1220, 4G50.) 



4450 Other functions whicli may be defined by linear 

 differential equations. {See also 4850.) 



4460 Other functions which may be defined by functional 

 equations. {See also 6030.) 



Differential Equations. 



4800 General. 



4810 Existence-theorems for ordinary and partial differential 

 equations. 



4820 Methods of solution and reduction of ordinary 

 differential equations. 



4830 Methods of solution and redaction of partial differen- 

 tial equations of the first order, including the 

 differentijil equations of theoretical d3'namics. 

 ■ 4840 Methods of solution and reduction 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 General theory of ordinary equations, not linear, 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 ; Pfaffians. 



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

 {See also 8450.) 



5230 Ti-ansformation of differential forms, including tan- 

 gential (or contact) transformations. 



5240 Differential invariants. {See also 1230, 1240.) 



Analytical Methods connected w^th Physical Problems. 



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



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



5620 Harmonic analysis; series other tlian Fourier's. 

 {See also 322U.) 



5630 Genei'alities on the differential equations of mathe- 

 matical physics. {See also B 2020.) 



5610 Integration of the differential equations of mathe- 

 matical physics b^' series. 



5650 Integration of the differential equations of mathe- 

 matical physics by definite integrals. 



5660 Dirichlet's problem and analogous problems, affected 

 by boundary conditions. 



