4420 



Bessel's Functions 



4420 



Associated functions, especially those of spheri- 



cal shell. Beltrami, E. Bologna Ac. Sc. 



Mm. 4 (1882) 211-. 

 Bessel's equation, general solution. Chessin, 



A. Am. J. Mth. 16 (1894) 186-. 

 -- and Biccati's equation. Greenhill, A. G, 



QJ. Mth. 16 (1879) 294-. 

 -- , tables of roots. Willson, E. W., & 



Peirce, B. 0. N. Y. Am. Mth. S. Bll. 3 



(1897) 153-. 



BESSEL'S FUNCTIONS. 



Schlomilch, 0. Schlomilch Z. 2 (1857) 137-. 

 Eayleigh, (Lord). Ph. Mg. 44 (1872) 328-. 

 Gegenbauer, L. WienAk. Sb. 70 (1874) M&.2) 



6-; 74 (1877) (Ab. 2) 124-; 75 (1877) (Ab.2) 



218- ; 88 (1884) (Ab. 2) 975-; 95 (1887) 



(Ab. 2) 409- . 



Hall, A. Des Moines Anal. 1 (1874) 81-. 

 Kapteyn, W. N. Arch. Wisk. 20 (1893) 116- ; 



Fschr. Mth. (1893-94) 849. 

 Gegenbauer, L. Mh. Mth. Ps. 8 (1897) 383-. 

 Macdonald, H. M. [1897] L. Mth. S. P. 29 



(1898) 110-. 



Nielsen, N. Kjrfb. Ov. (1899) 661- ; (1900) 



55. 

 addition and subtraction of arguments. Graf, 



J. H. Mth. A. 43 (1893) 136-. 

 and Cauchy's numbers, relation between. 



Chessin, A. S. A. Mth. 12 (1898-99) 170-. 

 connection with hyperspherical and spherical 



harmonics. Hobson, E. W. [1893] L. Mth. 



S. P. 25 (1894) 49-. 

 convergence of expansion of arbitrary function 



/ (x) in. Schlfifli, L. Mth. A. 10 (1876) 137-. 

 definite integrals connected with. Basset, A. B. 



Camb. Ph. S. P. 8 (1895) 122-. 

 development for effect of periodic forces. 



Schott, C. A. U. S. Coast Sv. Kp. (1862) 



232-. 

 developments. Meissel, E. As. Nr. 129 (1892) 



281- ; 130(1892) 363-. 

 expansion of function with 2 variables in. 



Cantor, G. [1871] Mth. A. 5 (1872) 133-. 

 -- any functions by. Neumann, C. Crelle 



J. 67 (1867) 310-. 



in series by. Konig, J. Mth. A. 17 (1880) 

 85. 



expression of function in terms of. Sheppard, 

 W. E. QJ. Mth. 23 (1889) 223-. 



' in semi-convergent series for large values of 

 variable. Callandreau, O. Bll. Sc. Mth. 

 14 (1890) 110-. 



formula, demonstration. Giuliani, G. G. Mt. 

 22 (1884) 201-. 



involving. Graf. J. H. Sch. Nf. Gs. Vh. 

 (1896) 59-. 



function related to. Lommel, E. C. J. [1875] 

 Mth. A. 9 (1876) 425-. 



integration of equation x m +* 2))t+i =t y = by. 



Lommel, E. Mth. A. 2 (1870) 624-. 

 formulas. Lerch, M. Prag Ceske Ak. Fr. 

 Jos. Rz. (Tfida 2) 5 (1896) Art. 23, 16 pp. ; 

 Fschr. Mth. (1896) 233-. 



integration formulas connected with. Gegen- 

 bauer, L. Mh. Mth. Ps. 5 (1894) 53-. 



1st kind. Wagner, C. Bern. Mt. (1894) 

 204-. 



. Gegenbauer, L. Mh. Mth. Ps. 10 



(1899) 189-. 



, addition theorem, generalisation. 

 Wendt, C. Mh. Mth. Ps. 11 (1900) 125-. 



and a continued fraction. Graf, I. H. 



A. Mt. 23 (1895) 45-. 



, roots, new properties. Gegenbauer, 

 L. Liege S. Sc. Mm. 2 (1900) No. 3, 

 7pp. 



and 2nd kinds. Nicolas, J. Par. EC. 

 Norm. A. 11 (1882) (Suppl.), 90 pp. 



, descending series for. McMahon, 



J. A. Mth. 8 (1893-94) 57-. 

 2nd kind. Gegenbauer, L. Wien Sb. 65 (1872) 



(Ab. 2) 33-; 66 (1872) (Ab. 2) 220-. 



. Bocher, M. A. Mth. 6 (1891-92) 85-. 



. Julius, V. A. Arch. Neerl. 28 (1895) 



221-. 



. Crelier, L. Bern. Mt. (1897) 61-. 



. Otti, H. Bern Mt. (1898) 1-. 



Neumann's researches. Schlafli, L. [1870] 



Mth. A. 3 (1871) 134-. 

 2nd order. Coates, C. V. QJ. Mth. 20 (1885) 



250- ; 21 (1886) 183-. 

 Oth order, roots. Bocher, M. N. Y. Am. Mth. 



S. Bll. 5 (1899) 385-. 

 and P-functions, roots. Van Vleck, E. B. 



Am. J. Mth. 19 (1897) 75-. 

 product J m (x)J n (x). Orr, W. McF. [1899] 



Camb. Ph. S. P. 10 (1900) 93-. 

 products and squares. Neumann, C. Mth. A. 



2 (1870) 192. 



properties. Hobson, E. W. L. Mth. S. P. 28 

 (1897) 370-. 



derived from continued fractions. Crelier, 

 L. A. Mt. 24 (1896) 131-. 



with purely imaginary index. Bocher, M. A. 



Mth. 6 (1891-92) 137-. 

 and related functions, roots. McMahon, J. 



A. Mth. 9 (1894-95) 23-. 

 representation of arbitrary functions by. Weber, 



H. [1872] Mth. A. 6 (1873) 146-. 



by definite integrals. Gubler, E. Ziir. 

 Vjschr. 33 (1888) 130-. 



of definite integrals by. Wagner, C. Bern 

 Mt. (1895) 115- ; (1896) 53-. 



roots. Bocher, M. N. Y. Am. Mth. S. Bll. 3 



(1897) 205-. 

 series, expression for a rational polynomial in. 



McMahon, J. Am. As. P. (1900) 42-. 

 solution of some differential equations by. 



Pearson, K. Mess. Mth. 9 (1880) 127-. 

 tables. Brit. Ass. Comm. B. A. Ep. (1889) 



28-; (1893) 227-; (1896) 98-. 

 theory. Lommel, E. C. J. [1870-79] Mth. A. 



3 (1871) 475-; 4 (1871) 103- ; 14 (1879) 510-; 

 16 (1880) 183-. 



_. Weber, H. Mth. A. 37 (1890) 404-. 

 . Meissel, E. As. Nr. 128 (1891) 435-. 

 , deduction of formulas. Ball, L. de. As. 

 Nr. 128 (1891) 1-. 



zero. Eudzki, M. P. Prace Mt.-Fiz. 3 

 69-; Fschr. Mth. (1892) 107-. 



343 



