1625 Finite Summation 



Triads. Fifteen girl problem, solution. Carp- 

 mael, E. L. Mth. S. P. 12 (1880-81) 148-. 



formed with 6 + l elements, systems. 

 Brunei, G. As. Fr. C. E. (1895) (Pt. 2) 

 145. 



6n - 1 and 6w - 2 elements. Brunei, 



G. Bordeaux S. Sc. PV. (1895-96) 40-. 



. Nine girl problem. Sylvester, J. J . Mess. 

 Mth. 22 (1893) 159-, 192. 



of once-paired elements. Homer, J. [1867] 

 QJ. Mth. 9 (1868) 15-. 



-7 and 15 things. Cayley, A. Ph. Mg. 



37 (1850) 50-. 

 Triangle of sequences. Andre, D. C. B. 118 



(1894) 575-, 726. 

 Vandermonde's theorem. Collins, E. [1839] 



St Pet. Ac. Sc. Bll. 6 (1840) 81-. 

 . Tanner, H. W. L. Mess. Mth. 25 (1896) 



, generalisation. Hill, M. J. M. Mess. 



Mth. 25 (1896) 154-. 

 Various theorems. Clausen, T. Crelle J. 4 



(1829) 278-. 

 Voting. Macfarlane, A. Edinb. Mth. S. P. 2 



(1884) 25-. 



1625 Finite Summation. Recur- 

 ring 1 series. 



Arithmetical formula. Netto, E. Mth. A. 49 

 (1897) 148. 



series. San Bertolo, N. Em. At. 10 (1856- 

 57) 78-. 



. Jung, V. Casopis 28 (1899) 281- ; 

 Fschr. Mth. (1899) 244. 



of different orders. Jarolimek, C. 6a- 



sopis 6 (*1877) 91-; Fschr. Mth. (*1877) 



176. 

 , sum of cubes of terms. Shidy, L. P. 



Des Moines Anal. 3 (1876) 51-. 

 , whose ultimate differences are constant. 



Pollock, (Sir) F. [1850] E. S. P. 5 (1851) 



852-. 

 Binomial expansion, summation of terms. 



Querret, . Gergonne A. Mth. 15 (1824-25) 



189-. 

 Combination sums of squares of even and odd 



numbers, relations. Oppolzer, T. von. Mth. 



A. 13 (1878) 405-. 

 Combinatory numbers, certain. Lemeray, . 



As. Fr. C. E. (1899) (Pt. 2) 99-. 



Continued product II (1 + i.c), expansion in 



i=0 



powers of x, coefficients. Schlafii, L. C. E. 

 25 (1847) 381- ; Grunert Arch. 10 (1847) 

 386-; 12 (1849) 53-; Crelle J. 43 (1852) 



Equations generating recurring series. Andre, 



D. Par. S. Mth. Bll. 6 (1878) 166-. 

 Expansion in recurring series, extension, and 



physical application. Topler, A. Steierm. 



Mt. (1872) 64-. 

 Factorial expression, summation. Cayley, A. 



Ph. Mg. 13 (1857) 419-. 



Figurate Numbers 1625 



Factorial expressions, transformations. Plarr, 



G. B. A. Ep. (1857) 101-. 

 Factorials, formula involving. Ellis, J. C. W. 



QJ. Mth. 8 (1867) 256-. 



Figurate numbers. 



Barruel, E. Par. EC. Pol. Cor. 2 (1809-13) 



220-. 

 Gergonne, J. D. Gergonne A. Mth. 4 (1813-14) 



115. 



Brassinne, E. N. A. Mth. 6 (1847) 120-. 

 Transon, A. (Prof.). N. A. Mth. 9 (1850) 255-. 

 Nicolaides, N. Les Mondes 7 (1865) 693-; 8 



(1865) 615-, 708-. 

 Le Cointe, J. L. A. Les Mondes 8 (1865) 



707-. 



Soufflet, . Les Mondes 13 (1867) 336-. 

 Hochheim, A. Arch. Mth. Ps. 55 (1873) 



189-. 

 formulae, proofs. Stegmann, F. Grunert Arch. 



5 (1844) 82-. 

 new method. Nicholson, P. Tilloch Ph. Mg. 



53 (1819) 412-. 

 polygonal numbers. Gough, J. Nicholson J. 



20 (1808) 161-. 

 . Barlow, P. Nicholson J. 21 (1808) 



118-. 

 . Gough, J. Nicholson J. 21 (1808) 



241-. 

 . Barlow, P. Nicholson J. 22 (1809) 



33. 



. Musso, G. G. Mt. 31 (1893) 173-. 



. Catalan, E. G. Mt. 31 (1893) 227-. 



. Berger, A. Ups. S. Sc. N. Acta 17 



(1898) No. 4, 38 pp. 

 , Fermat's theorem. Pollock, (Sir) F. 



Phil. Trans. (1861) 409- ; E. S. P. 13 (1864) 



542-. 

 , . Pepin, T. Em. N. Line. At. 46 



(1893) 119-. 

 , , extension. Pollock, (Sir) F. 



[1850] E. S. P. 5 (1851) 922-. 

 , , . Maillet, E. Par. S. Mth. 



Bll. 23 (1895) 40-; Liouv. J. Mth. 2 (1896) 



363-. 

 , , general proof. Cauchy, A.L. Par. 



Mm. de PL (1813-15) 177-. 

 , formula for. Laisant, C. A. Par. S. 



Phlm. Bll. 3 (1891) 29-. 

 polyhedral numbers. Giudice, . Palermo 



Cir. Mt. Ed. 3 (1889) 231. 

 sums. Brassinne, E, N. A. Mth. 6 (1847) 



120-. 

 theorem. Bjorling, E. G. Grunert Arch. 7 



(1846) 266-. 



triangular numbers. Casinelli, A. (s. L.) Bo- 

 logna N. Cm. 2 (1836) 415-. 

 , summation of like powers of first n. 



Barbette, E. Mathesis 15 (1895) 111-. 

 , theorems. Liouville, J. Liouv. J. Mth. 



7 (1862) 407- ; 8 (1863) 73-. 

 , . Glaister, J. W. L. Mess. Mth. 5 



(1876) 164-. 

 trigonal numbers. Stern, M. A. Crelle J. 69 



(1868) 370-. 



89 



