4420 



Spherical Harmonics 



4420 



Frischauf, J. Crelle J. Mth. 107 (1891) 87-. 

 Caspary, F. Crelle J. Mth. 107 (1891) 137- ; 



Par. S. Mth. Bll. 19 (1891) 11-. 

 Besso, D. G. Teix. J. Sc. 12 (1895) 65-; 



Fschr. Mth. (1893-94) 818. 

 Gegenbauer, L. Mh. Mth. Ps. 7 (1896) 35-. 

 Rogel, F. Prag Sb. (1898) (Mth.-Nt.) No. 30, 



3 pp. 



Tallqvist, H. Helsingf. Acta 26 (1900) No. 4, 



87pp. 

 application. NiemiJller, F. Z. Mth. Ps. 24 



(1879) 57-. 



to Mittag-Leffler's theorem, and to deter- 

 mination of functions with lacunae. 

 Pincherle, S. Bologna Ed. (1883) 100-. 



of principle of maximum and minimum 

 exponents to determination. Mazing, A. 

 [1891] Kec. Mth. (Moscou) 16 (1893) 173-. 



to Segner's numbers. Caspary, F. Brux. 

 Mm. Cour. 4, 52 (1890-93) No. 8, 15 pp. 



of theorem in differentiation. Hobson, E. 

 W. [1892] L. Mth. S. P. 24 (1893) 55-. 



and associated functions. Basset, A. B. Mess. 

 Mth. 13 (1884) 147-. 



cylindrical functions. Olbricht, R. Ac. 

 Nt. C. N. Acta 52 (1888) 1-. 



definite integrals connected with. Frost, P. 



QJ. Mth. 19 (1883) 242-. 

 as determinants. Heun, K. Gott. Nr. (1881) 



104-. 



. Kronecker, L. Gott. Nr. (1881) 271-. 



determination of Green's function. Dougall, J. 



Edinb. Mth. S. P. 18 (1900) 33-. 

 differentiation. Gallop, E. G. [1896] L. Mth. 



S. P. 28 (1897) 183-. 

 expression for. Dougall, J. Edinb. Mth. S. 



P. 8 (1890) 81-. 

 extension. Pincherle, S. Bologna Ac. Sc. 



Mm. 1 (1890) 337-. 



formula. Fujisawa,R. Mess. Mth. 21 (1892) 40-. 

 functions analogous to. Giuliani, G. G. Mt. 



25 (1887) 203-. 

 general form. Dedekind, R. Ziir. Vjschr. 4 



(1859) 346-; 5 (1860) 66-. 

 generalisation. Pincherle, S. Bologna Ed. 



(1891-92) 31-. 

 identities in connexion with. Vivanti, G. Z. 



Mth. Ps. 36 (1891) 1-. 

 any index, expression and expansion. 



Lyetnikov, A. V. (xn) Eec. Mth. (Moscou) 



10 (1882-83) (Pt. 1) 383-. 

 2nd kind, roots. Hermite, C. Toul. Fac. Sc. 



A. 4 (1890f I, 10 pp. 

 , . Stieltjes, T. J. Toul. Fac. Sc. A. 



4 (1890) J, 10 pp. 



, . Hermite, C. Prag Ab. 4 (1892) 



No. 2, 10 pp. 

 logarithms of 1st five orders for every 5 degrees. 



Schmidt, A. Terr. Mag. 1 (1896) 73-. 

 higherorder. Giuliani,G. G.Mt. 26 (1888)155-. 

 property. Clebsch, A. [1861] Crelle J. 60 



(1862) 343-. 

 representation by an integral. Walter, A. 



Steierm. Mt. (1887) 25-. 

 roots of equations occurring in. Markoff, A. 



Mth. A. 27 (1886) 143-, 177-. 

 series. Dint, U. [1873] A. Mt. 6 (1875) 112-, 



series, convergence. Frischauf, J. Steierm. 



Mt. (1886) 3-. 



, and their differentials, tables for approxi- 

 mate evaluation. Schmidt, A. Terr. Mag. 



4 (1899) 59-. 

 theorems. Pizzetti, . Palermo Cir. Mt. Ed. 



13 (1899) 89-. 

 , generalisation. Gegenbauer, L. Palermo 



Cir. Mt. Ed. 13 (1899) 92-. 

 theory. Schendel, L. Crelle J. Mth. 80 (1875) 



86-; 82 (1877) 158-. 



. Hermite, C. C. E. 86 (1878) 1515-. 

 . Frischauf, J. Steierm. Mt. (1886) 19-. 

 , extension. Frombeck, H. Wien Ak. Sb. 



70 (1874) (Ab. 2) 61-. 

 transformation of coordinates. Schmidt, A. 



Z. Mth. Ps. 44 (1899) 327-. 

 one variable, coefficients. Bauer, G. Crelle 



J. 56 (1859) 101-. 

 , and coefficients of series of spherical 



functions. Winckler, A. [1860] Wien D. 



21 (1863) 37-. 

 P(jji), regarded as a function of n, zeros. 



n Macdonald, H. M. [1899] L. Mth. S. P. 



31 (1900) 264-. 



Theory of potential, expansion in series in. 

 Johamon, A. M. Ups. Arsk. (1893) (Mt. Nt.) 



Zonal harmonics, table. Perry, J. [1890] L. 



Ps. S. P. 11 (1892) 221- ; Ph. Mg. 32 (1891) 



512-. 

 -- , , corrections to Perry's. Farr, C. C. 



Ph. Mg. 49 (1900) 572. 

 [1 - a cos <(> + a' 2 ] A d<t>, integration. Moth, F. X. 



As. Nr. 4 (1826) 539-. 

 (1 - 2a cos <t> + a 2 ) ~ ^, expansion in powers of a, 



coefficients. Plana, G. Zach Cor. 14 (1826) 



125-. 

 (1 -2xz + z 2 )"^, expansion. Ivory, J. Liouv. 



J. Mth. 2 (1837) 105-. 



, . Liouville,J. Liouv. J. Mth. 2 (1837)135-. 



, in powers of z. Schaar, M. Brux. Ac. 

 Bll. 15 (1848) (pte. 2) 506-. 



F( n ', application to phenomena which are 



functions of latitude and longitude. 



Neumann, F. E. As. Nr. 15 (1838) 313-. 

 (1 - 2at + a 2 ) ~ i, expansion by definite integrals. 



Dirksen, E. H. Berl. B. (1843) 111-. 

 [a 2 - 2aa' (cos w cos <f> 



+ sin a> sin <f> cos (6 - 0')) + a' 2 ] ~ *, 



expansion. Jacobi, C. G. J. Crelle J. 26 



(1843) 81-. 



sin 





transformation. Liouville, J. Liouv. J. 

 Mth. 11 (1846) 458-. 



l + *. v + X ( X + V v + &c> ad inf _ ScMffer, . 



y y(y + i) 



Crelle J. 37 (1848) 127-. 

 Y n , series, convergence. Bonnet, 0. C. E. 



28 (1849) 349-, 378-. 

 and X n , expansion in series of. Bonnet, O. 



Liouv. J. Mth. 17 (1852) 265-. 



348 



