Harmonic Analysis; Series other than Fourier's 



5620 



5620 Harmonic analysis; series 

 other than Fourier's. Spheri- 

 cal and ellipsoidal harmonics. 

 (See also 3220.) 



Cylindrical functions, development of zero in 

 series of. Nielsen, N. Mth. A. 52 (1899) 

 582-. 



, integrals, and Fourier series. Hankel, H. 



[1869] Mth. A. 8 (1875) 471-. 



Ellipsoidal harmonics. Niven, W. D. [1890] 

 Phil. Trans. (A) 182 (1892) 231-. 



Expansion of given function in series according 

 to harmonic functions. Steklov,V.A. Khar- 

 kov Mth. S. Com. 5 (1896?) 60-; Fschr. Mth. 

 (1896) 203- ; C. B. 128 (1899) 279-. 



{JS 2 - 2Rr [cos u cos u' cos (x - x') 



+ sin u sin u' cos (y - y')] + r 2 }" 1 . 

 Stieltjes, T. J. Liouv. J. Mth. 5 (1889) 55-. 



Fourier-Bessel functions, representation of 

 arbitrary function by. Harnack, A. Leip. 

 Mth. Ps. B. 39 (1887) 191-. 



Functional series, expansion of function in. 

 Johnson, A. R. Mess. Mth. 15 (1886) 81-. 



Functions X, Y, etc., possessing property that 

 = 0, and expansible in form aX + pY 



. , construction. Routh, E. J. L. 



Mth. S. P. 10 (1878-79) 146-. 

 Fundamental functions and expansion in terms 



of them. Renaux, . C. B. 129 (1899) 



545-. 

 Harmonic analysis. Perry, J., & Hunt, H. F. 



L. Ps. S. P. 14 (1896) 1-; Ph. Mg. 40 (1895) 



506-. 

 , application to dynamical theory of tides. 



Hough, S. S. Phil. Trans. (A) 189 (1897) 



201-. 



expression of daily variation of solar radia- 

 tion, etc. Hargreaves, R. Camb. Ph. S. P. 

 9 (1898) 532-. 



functions for elliptic cone. Hobson, E. W. 

 L. Mth. S. P. 23 (1892) 231-. 



, expansion of arbitrary function in series 



of. Zaremba, S. C. B. 128 (1899) 1088-. 

 of Poincare. Stekloff, W. Toul. Fac. 



Sc. A. 2 (1900) 273-. 

 , theorem. Arone, G. D. d\ C. B. 114 



(1892) 1055-. 

 of 3 variables, analogous to 0-Fuchsian 



functions. Stouff, X. Toul. Fac. Sc. A. 4 



(1890) A, 15 pp. 

 , new theorems. Sanctis, L. de. 



A. Mt. 4 (1900) 161-. 

 several real variables. Arone, G. D. d\ 



C. B. 118 (1894) 342-. 

 periodic infinite series, summation. Raabe, 



J. L. Crelle J. 23 (1842) 105- ; 25 (1843) 



160-. 



series with infinitely small terms. Fontana, 

 G. Verona S. It. Mm. 2 (1784) 123-. 



Harmonics of a ring. Niven, W. D. L. Mth. 



S. P. 24 (1893) 272-. 

 Lame's equation. Escary, . C. B. 91 (1880) 



40-, 102-. 



Lame's and spherical functions, expansion by. 



Lindemann, C. L. F. [1881] Mth. A. 19 



(1882) 323-. 

 Laplace's coefficients. Glaisher, J. W. L. L. 



Mth. S. P. 6 (1874-75) 126-. 

 . Hall, A. A. Mth. 3 (1887) 1-. 



, equation of. Moon, R. Ph. Mg. 40 

 (1870) 434-. 



, expansion, determination of numerical 



factors in. Tarleton, F. A. Ir. Ac. P. 1 



(1889-91) 16-. 

 and functions. Heath, D. D. OJ. Mth. 



7 (1866) 23-. 

 , proof that F (p, u) may be expanded into 



a series of. Procul. [Pseudon.] (vi Adds.) 



Ph. Mg. 25 (1844) 337-. 

 , transformation. Plarr, G. Edinb. B. 



S. T. 36 (1892) 19-. 



values of integral I Q n Q n 'dfj., Q n> Q n > 



J o 



being Laplace's coefficients of orders n, n', 

 with application to theory of radiation. 

 Rayleigh, (Lord). Phil. Trans. 160 (1870) 

 579-. 



, F (0, !/<) developable in only one series of. 



Pratt, J. H. Ph. Mg. 8 (1836) 474-. 



b ( ^, use of continued fractions in calcu- 

 lation. Callandreau, O. Par. EC. Pol. J. 

 cah. 45 (1878) 91-. 



dynamical equations, general integration. 

 Hough, S. S. [1897] Phil. Trans. (A) 191 

 (1898) 139-. 



functions. Cayley, A. Liouv. J. Mth. 13 

 (1848) 275-. 



. Schlafli, L. A. Mt. 1 (1867-68) 

 243-. 



, Dirichlet's proof of expansion possibility. 



Poincare, H. C. B. 118 (1894) 497-. 



, expansion of arbitrary function in. 

 Echols, W. H. A. Mth. 12 (1898-99) 164-. 



, fundamental principle, geometrical 

 proof. Pratt, J. H. Ph. Mg. 24 (1862) 

 504-. 



of higher order, development of function 



of several variables according to. Mehler, 

 F. G. Crelle J. 66 (1866) 161-. 



, property. Smith, Arch. Camb. Mth. J. 



2 (1841) 192. 



, series expressing. Darboux, G. Liouv. 



J. Mth. 19 (1874) 1-. 



integrals, definite integrals allied to. Un- 

 ferdinger, F. Wien Sb. 55 (1867) (Ab. 2) 

 90-. 



Legendre's functions, expansion of potential 

 function l/B*-i in. Routh, E. J. L. Mth. 

 S. P. 26 (1895) 481-. 



Linear, cylindric, spherical, and allied func- 

 tions, expansion of functions in terms of. 

 Alexander, P. Edinb. E. S. T. 33 (1888) 

 313-. 



Periodic series, expansion of function. Encke, 

 J. F. Berl. As. Jb. (1860) 313-. 



. , sums, critical values. Stokes, G. G. 

 [1847] Camb. Ph. S. T. 8 (1849) 533-. 



Potentials of ellipsoid and ellipse, expansion in 

 series. Niven, W. D. Phil. Trans. 170 

 (1880) 379-. 



403 



cc 2 



