Glaisher] 



329 



[Glaisher 



Expressions for 6 (x) as a definite integral. Messenger 



Math., 17, 1888, 152-153. 



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. & Phys. Sci. Sect. 



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

 Note on series whose coefficients involve powers of the 



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



146. 

 Expansions of K, I, G, E in powers of k" 2 -k 2 . 



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



C 1 T{ T 

 On the expansion of =, , -=, etc., in ascending powers 



K. Cr -Ci 



of fc 2 . Messenger Math., 19, 1890, 164-174. 



On the square of EULEB'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 g-series derived from the elliptic and zeta 



functions of \K and %K. [1890.] London Math. Soc. 

 Proc., 22, 1891, 143-171. 



Relations between the divisors of the first n 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 IK. Messenger Math., 

 20, 1891, 191-192. 



On the sums of the inverse powers of the prime 



numbers. Quart. Jl. Math., 25, 1891, 347-362, 384. 

 Calculation of the hyperbolic logarithm of IT to thirty 



decimal places. Quart. Jl. Math., 25, 1891, 362-368, 



384. 

 On the series i + i + i + f + T V + etc. Quart. Jl. Math., 



25, 1891, 369-375. 

 On the series i-i + | + Ar- T V- etc - Quart. Jl. Math., 



25, 1891, 375-383. 

 Expression for the sum of the cubes of the divisors of 



a number in 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 cr(n). Messenger 

 Math., 21, 1892, 122-130. 



On the connexion between recurring formulae involving 

 sums of divisors and the corresponding formulas involving 

 differences between sums of even and uneven divisors. 

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



Note on Mr. KLEIBER'S functions K t 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 - fc 2 . Messenger Math., 

 22, 1893, 109-144. 



Values of integrals in terms of fc 2 . Messenger Math., 



22, 1893, 145-158. 



- On the series __- + _ + - ^ - etc. Quart. Jl. 

 Math., 26, 1893, 33-47. 

 R. S. XV. 



_ 



On the series + -f 4-^-TV + etc. Quart. Jl. Math., 



26, 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, 



176-184. 

 On the constant which occurs in the formula for 



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

 Note on a relation connecting constants analogous to 



EULER'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 terms 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, 152-182; 27, 



1898, 20-98. 

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



1898, 1-168. 

 General summation-formulae in finite differences. 



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



124 x - 1 

 Table of the values of 5 . 5 .=... , the deuomi- 



t O O 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 formula involving Bernoullian 



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

 Divisibility 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 n + 2 n + ... +x n and 



l-2 n +...a; n . Quart. Jl. Math., 30, 1899, 166-204. 

 On the residue with respect to p n+1 of 'a binomial- 

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



30, 1899, 349-360. 



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 Bernoullian 



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 



top 3 . Quart. Jl. Math., 31, 1900, 110-124. 



On the value of the series 



x n + (x -q) n + (x - 2q) n + ... +r n 



and x n -(x-q) n +(x-2q) n - ...r n . 



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

 On l n (x-l) n + 2 n (x-2) n +... + (x-l) n l n and other 



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

 A congruence theorem relating to the Bernoullian 



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



42 



