5610 



Harmonic Analysis; Fourier's Series 



5610 



Expansion of /(, u') in series of sines and 



cosines of multiples of u and u'. Bessel, F. W. 



Berl. Ab. (1820-21) 55-. 

 <f>(x) in sines and cosines of multiples of 



x. Bessel, F. W. As. Nr. 16 (1839) 229-. 

 Expansions of functions employed in physics, 



general reason for use. Boussinesq, J. C. E. 



92 (1881) 513-. 

 implicit functions in trigonometric series, 



and their transformation to isotropic means. 



Cauchy, A. L. C. E. 38 (1854) 910-. 



in series of multiple sines and cosines. 

 Cayley, A. Camb. Mth. J. 3 (1843) 162-. 



particular solutions of equations of 



elasticity. Lauricella, G. Tor. Ac. Sc. At. 



34 (1898) 11-. 

 , trigonometric. Lerch, . Toul. Fac. Sc. 



A. 3 (1889) C, 11 pp. 

 , , of periodic solutions of V 2 F = 0. Appell, 



P. C. B. 102 (1886) 1439- ; Liouv. J. Mth. 



3 (1887) 5-. 



Fourier's double integral theorem. Glaisher, 

 J. W. L. Mess. Mth. 2 (1873) 20-. 



, Boole's and other proofs. Alex- 

 ander, P. Edinb. Mth. S. P. 3 (1885) 45-. 



, failing cases. Alexander, P. Edinb. 



Mth. S. P. 3 (1885) 12-. 



integrals, more general theorem. Griln- 



ivald, F. K. Z. Mth. Ps. 9 (1864) 131-. 



expansion for doubly periodic functions, new 

 method. Mohrmann, G. Arch. Mth. Ps. 

 12 (1894) 1-. 



expansions of functions in trigonometric 

 series. Tliomson, (Sir) W. Camb. Mth. J. 



2 (1841) 258-. 



transcendent functions. Krygowski, 



Z. Prace Mt.-Fiz. 5 (1894) 70-. 



formula and its analogues. Pellet, A. C. 

 E. 106 (1888) 1062-. 



applied to differentiation. Liouville, J. 



Crelle J. 13 (1835) 219-. 



generalised. Liouville, J. Liouv. J. 

 Mth. 1 (1836) 102-. 



integrals. Du Bois-Reymond, P. Mth. A. 



4 (1871) 362-. 



problem. LeRoy,E. C. R. 120 (1895) 179-. 



theorem. Gregory, D. F. Camb. Mth. J. 



3 (1843) 288-. 



. La Vallee-Poussin, C. de. Brux. S. 



Sc. A. 15 (1891) (Ft. 1) 39-. 

 , general extension. Preston, T. Ph. Mg. 



43 (1897) 281-. 

 , generality of new theorem analogous to. 



Stoney, G. J. Ph. Mg. 43 (1897) 139-. 

 , proof. Bonnet, 0. N. A. Mth. 3 (1844) 



, . Walton, W. [1865] QJ. Mth. 8 



(1867) 136-. 

 , , Cauchy's. Schouten, G. N. Arch. 



Wisk. 18 (1891) 146-. 

 and sin oo and cos oo . Moon, R. Ph. 



Mg. 26 (1845) 483-. 



theorems. Hobson, E. W. Mess. Mth. 11 

 (1882) 11-. 



, proof. Schldmilch, 0. Crelle J. 36 



(1848) 268-. 

 Functions expressible by series of periodic terms. 



Ivory, J. Ph. Mg. 9 (1836) 161-. 



Harmonic analyser, Henrici and Coradi's. 

 Grabowski, L. Wiad. Mt. 4 (1900) 236-. 



components, computation (for yearly and 

 daily periods). Strachey, (Lt.-Gen.) R. B. 

 S. P. 42 (1887) 61-. 



of periodic motion. Clifford, W. K. 



[1873] (vn) Mess. Mth. 3 (1874) 153-. 



curves, graphic analysis. Wedmore, E. B. 

 Elect. 35 (1895) 512-. 



decomposition of functions, and allied ex- 

 pansions. Johnson, A. R. L. Mth. S. P. 

 19 (1889) 75-. 



expansion of arbitrary function. Zaremba, S. 

 Liouv. J. Mth. 6 (1900) 47-. 



series. Schldmilch, O. Z. Mth. Ps. 14 

 (1869) 250-. 



. Cesdro, E. (xn) Mathesis 1 (1881) 



51-, 80, 143-. 



Integral formulas representing arbitrary func- 

 tions, range of application. Du Bois-Rey- 

 mond, P. [1874] Crelle J. Mth. 79 (1875) 38-. 



Ae~ ar 

 Neumann's potential function S . Bel- 



trami, E. Em. E. Ac. Line. Ed. 4 (1895) 

 (Sem. 2) 177-. 



Periodic curves, analysis. Wedmore, E. B. 

 I. Elect. E. J. 25 (1897) 224-. 



function cos x - % cos 3x + % cos 5x etc. Wil- 

 braham, H. Camb. and Dubl. Mth. J. 3 

 (1848) 198-. 



A + A l cos<f> + B 1 sin <f>... + A n cos n<f> 

 + B n sin n<f>, transformation. Stieltjes, T. J. 

 (jun.) N. Arch. Wisk. 9 (*1882) 111-. 



series, summation. Raabe, J. L. Crelle J. 

 15 (1836) 355-. 



, value at certain limits. Newman, F. W. 



Camb. and Dubl. Mth. J. 3 (1848) 108-. 

 Periodicities, investigation of hidden, with 



application to supposed 26 day period. 



Schuster, A. Terr. Mag. 3 (1898) 13-. 

 , lunar and solar, of earthquakes. Schuster, 



A. Nt. 56 (1897) 321. 



in series of observations, method of ascer- 

 taining. Nene.V.N. B. S. P. 36 (1884) 361-. 



Phases of function, calculation. Cabreira, A. 



[1900] Lisb. J. Sc. Mth. 6 (1902) 55-. 

 Series of sines and cosines of multiple angles, 



numerical values of coefficients. Lubbock, 



J. W. Ph. Mg. 33 (1848) 106-. 

 Summation of periodic functions. Gylden, 



J. A. H. (x) Stockh. Ak. Hndl. 11 (1872) 



No. 1, 15 pp. ; Par. EC. Norm. A. 8 (1879) 



203-. 

 Trigonometric series, convergence for arbitrary 



function between given limits. Lejeune- 



Dirichlet, G. Crelle J. 4 (1829) 157- ; 17 



(1837) 35-. 

 , representation of arbitrary functions by. 



Lejeune-Dirichlet, G. Epm. Ps. 1 (1837) 



152-. 

 , . Harnack, A. Mth. A. 



17 (1880) 123-. 

 Wave motion, supposed proof of theorem in. 



Stoney, G. J. Ph. Mg. 43 (1897) 368- ; 44 



(1897) 98-, 206-. 

 , . Preston, T. Ph. Mg. 43 



(1897) 458-. 



402 



