Glaisher] 



329 



[Glaisher 



Expressions for O (.r) as a definite integral. Messenger 



Math., 17, 1888, 1.52-153. 

 On the expansions of the theta functions in ascending 



powers of the argument. [1887.] Cambridge Phil. Soc. 



Proc. , 6, 1889, 96-98. 

 On expressions for the theta functions as definite 



integrals. [1887.] Cambridge Phil. Soc. Proc, 6, 1889, 



129-134. 

 On the series which represent the twelve elliptic and 



the four zeta functions. Messenger Math., 18, 1889, 



1-84. 

 . [Presidential address to the Math. & Pliys. Sci. Sect. 



General considerations.] Brit. Ass. Eep., 1890, 719-727. 

 Note on series whose coefficients involve powers of the 



BernouUian numbers. Messenger Math., 19, 1890, 138- 



146. 

 Expansions of K, I, G, B in powers of k"--k^. 



Messenger Math., 19, 1890, 146-150. 

 C h' T 

 On the expansion of :p^,-p, etc., in ascending powers 



K ir J^ 



of k\ Messenger Math., 19, 1890, 164-174. 



On the square of Euleu's series. [1889.] London 



Math. Soc. Proc, 21, 1891, 182-215. 



On the function which denotes the excess of the 



number of divisors of a number which = 1, mod. 3, over 

 the number which =2, mod. 3. [1890.] London Math. 

 Soc. Proc, 21, 1891, 395-402. 



. On the (/-series derived from the elliptic and zeta 



functions of fjK and JA'. [1890.] London Math. Sue. 



Proc, 22, 1891, 143-171. 

 Relations between the divisors of the first m numbers. 



London Math. Soc Proc, 22, 1891, 359-410. 

 Theorem relating to sums of even powers of the 



natural numbers. Messenger Math., 20, 1891, 120-128. 

 Recurring relations involving sums of powers of 



divisors. Messenger Math., 20, 1891, 129-135, 177-181 ; 



21, 1892, 49-64. 

 Note on the sums of even powers of even and uneven 



numbers. Messenger Math., 20, 1891, 172-176. 



On the elliptic functions of |A'. Messenger Math., 



20, 1891, 191-192. 



On the sums of the inverse powers of the prime 



numbers. Quart. Jl. Math., 25, 1891, 347-302, 384. 

 Calculation of the hyperbolic logarithm of jr to thirty 



decimal places. Quart. Jl. Math., 25, 1891, 362-308, 



384. 

 On the series J^ + ^ + i + f -l-yV + E'''- Quai'- Jl- Math., 



25, 1891, 369-375". 

 On the series i - i + f + yV " tV - etc. Quart. Jl. Math., 



25, 1891, 37-5-383. 

 Expression for the sum of the cubes of the divisors of 



a number m terms of partitions of inferior numbers. 



Messenger Math., 21, 1892, 47-48. 

 : Expressions for symmetrical functions of /, G, E 



in terms of q. Messenger Math., 21, 1892, 65-69. 

 Note on a recurring formula for a(n). Messenger 



Math., 21, 1892, 122-130. 

 On the connexion between recurring formuhv involving 



sums of divisors and the corresponding formuhe involving 



differences between sums of even and uneven divisors. 



Phil. Mag., 33, 1892, 54-61. 

 Note on Mr. Kleibee's functions A'^ and G;. Mes- 

 senger Math., 22, 1893, 71-82. 



On certain series and definite integrals. Messenger 



Math., 22, 1893, 97-109. 



Developments in powers of fc'2 - U-, Messenger Math., 



22, 1893, 109-144. 

 Values of integrals in terms of k-. Messenger Math., 



22, 1893, 145-158. 



On the series 5:, - ^. + ;jt, -t- :pfT. - -.-js - etc. Quart. Jl. 



3'- 5- 

 Math., 26, 1893, 33-47. 



K. S. XV. 



7- 11- 13- 



On the series i-l-i-}-J-Tir-T>3-t- etc Quart. Jl.Math., 



20, 1893, 48-65. " 

 Note on the law of frequency of prime numbers. 



Messenger Math., 23, 1894, 97-107. 

 On certain numerical products in which the exponents 



depend upon the numbers. Messenger Math. , 23, 1894, 



145-175; 25, 1896, 186. 

 On series involving inverse even powers of subeven 



and supereven numbers. Messenger Math., 23, 1894, 



1,76-184. 

 On the constant which occurs in the formula for 



l'.2-'.3^...n". Messenger Math., 24, 1895, 1-16. 

 Note on a relation connecting constants analogous to 



Edlek's constant. Messenger Math., 24, 1895, 24-27. 

 Expressions for gamma functions in terms of complete 



elliptic integrals. Messenger Math., 24, 1895, 27-47. 

 Summation of series in which the rth term is the 



reciprocal of the product of the members of the rth set 



of n consecutive terras in an arithmetical progression. 



Messenger Math., 24, 1895, 124-171. 

 Products and series involving prime numbers only. 



Quart. Jl. Math., 27, 1895, 270-237; 28, 1896, 1-174. 

 On the definite integrals connected with the Bernoul- 



lian function. Messenger Math., 26, 1897, 1.52-182; 27, 



1898. 20-98. 

 The BernouUian function. Quart. Jl. Math., 29, 



1898, 1-168. 

 General summation -formulae in finite differences. 



Quart. Jl. Math., 29, 1898, 303-328. 



Table of the values of -- . 7, . ^ ... , the denomi- 



2 3 5 X 



nators being the series of prime numbers. Messenger 



Math., 28, 1899, 1-17. 

 Note on a theorem relating to sums of even powers 



of the natural numbers. Messenger Math., 28, 1899, 



29-32. 

 Classes of recurring formuliB involving BernouUian 



numbers. Messenger Math. , 28, 1899, 36-79. 

 Divisibihty of the sum of the products of the first 



n numbers taken r together. Messenger Math., 28, 1899, 



184-186. 

 On the residue of a binomial-theorem coefficient with 



respect to a prime modulus. Quart. Jl. Math., 30, 1899, 



150-156. 

 On the sums of the series l"-(-2''-^ ... -fx" and 



1" -2" -(-... .T''. Quart. Jl. Math., 30, 1899, 166-204. 

 On the residue with respect to y"+' of a binomial- 

 theorem coefficient divisible by p". Quart. Jl. Math., 



30, 1899, 349-300. 

 A congruence theorem relating to sums of binomial- 

 theorem coefficients. Quart. Jl. Math., 30, 1899, 361- 



383. 

 On a congruence theorem relating to an extensive 



class of coefficients. London Math. Soc. Proc, 31, 1900, 



193-215. 

 On a set of coefficients analogous to the Eulerian 



numbers. London Math. Soc. Proc, 31, 1900, 216-235. 

 Fundamental theorems relating to the BernouUian 



numbers. Messenger Math., 29, 1900, 49-63, 129-142. 

 Congruences relating to the sums of products of the 



first n numbers and to other sums of products. Quart. 



Jl. Math., 31, 1900, 1-35. 

 Residues of binomial-theorem coefficients with respect 



toy-*. Quart. Jl. Math., 31, 1900, 110-124. 



On the value of the series 



a-"-!- (.r - 7)"-!- (.c - 2(;)''-l- ... -fr" 



and .r"- (j; - q)''+{x - 2(/)'' - ... r''. 



Quart. Jl. Math., 31, 1900, 193-227. 

 On l(,r-l)''-f 2"(.c-2)-^...-)-(.r-l)"l" and other 



similar series. Quart. Jl. Math., 31, 1900, 241-247. 

 A congrueuce theorem relating to the BernouUian 



numbers. Quart. Jl. Math., 31, 1900, 253-263. 



42 



