0810 Calculus of Operations 



Calculus of operations, notes. Studnicka, F. 



Prag Sb. (1871) (pt. 2) 39-. 

 , problem. Westergaard, H. (xn) Ts. 



Mth. 6 (1876) 37-. 



, supplement. Paterson, J. [1874] 

 Alb. I. T. 8 (1876) 191-. 



, theorem. Walton, W. QJ. Mth. 3 



(1860), 278-, 314-. 

 , and applications. Greer, H. R. 



QJ. Mth. 3 (1860) 148-. 

 , , note. Roberts, S. QJ. Mth. 3 



(1860) 310-. 

 , theorems. Donkin, W. F. Camb. 



and Dubl. Mth. J. 5 (1850) 10-. ' 

 , . Spottiswoode, W. Camb. and 



Dubl. Mth. J. 8 (1853) 25-. 



, . Carmichael, R. Camb. and 

 Dubl. Mth. J. 8 (1853) 165-. 



; . Crofton, M. W. QJ. Mth. 16 



(1879) 323-. 

 , . Walker, J. J. [1880-81] 



L. Mth. S. P. 11 (1879-80), 108- ; 12 



(1880-81) 193-. 

 , , general, and applications. Warren, 



J. W. [1861] QJ. Mth. 5 (1862) 29-. 

 symbols. Spottiswoode, W. Phil. Trans. 



(1862) 99-. 

 , applications to differential equations. 



Russell, W. H. L. Phil. Trans. (1861) 69- ; 



(1862) 253- ; (1863) 517-. 

 , to non-linear differential equations. 



Russell, W. H. L. E. S. P. 13 (1864) 423-. 

 , to partial differential equations. 



Russell, W. H. L. E. S. P. 13 (1864) 432-. 



, division, internal and external. 

 Spratt, T. A. B. E. S. P. 11 (1860-62) 

 557-. 



, recent discoveries. Russell, W. H. L. 



B. A. Kp. (1862) (pt. 2) 7-. 

 Complete system of polar mutually permutative 



operations. Gapelli, A. Nap. Ed. 32 (1893) 



29-, 155-. 



De Morgan's extension of the algebraic pro- 

 cesses (symbolic algebra). Ladd, C. Am. 



J. Mth. 3 (1880) 210-. 

 Determinants, Smith's. Mansion, P. (xn) 



Brux. S. Sc. A. 2 (1878) (Pt. 2) 211-. 

 Differentials of symbolic expressions. Lipschitz , 



R. Berl. Ak. Sb. (1899) 122-. 

 Differentiation with fractional indices, and 



differentiation, general. Center, W. Camb. 



and Dubl. Mth. J. 3 (1848) 274-; 4 (1849) 



21-; 5 (1850) 206-. 



generalised. Moritz, R. E. N. Y. Am. 

 Mth. S. Bll. 6 (1900) 184, 185-. 



Distributive functional calculus. Pincherle, S. 



Mil. I. Lomb. Ed. 30 (1897) 1031- ; Mth. A. 



49 (1897) 325-. 

 operations. Pincherle, S. Em. E. Ac. 



Line. Ed. 4 (1895) (Sem. 1) 142-. 

 . Calo, B. Em. E. Ac. Line. Ed. 4 



(1895) (Sem. 2) 52-. 



operations differing by permutation from a 

 given operation. Pincherle, S. Tor. Ac. 

 Sc. At. 30 (1895) 820-. 



Divisibility by a polynomial, extension of the 

 conception. Pincherle, S. Em. E. Ac. 

 Line. Ed. 7 (1898) (Sem. 1) 185-. 



Calculus of Operations 0810 



Equations analogous to differential equations. 



Bourlet, C. C. E. 124 (1897) 1431-. 

 . Appell, P. C. E. 124 (1897) 



1433-. 

 Exponential formula giving sum of sines or 



cosines of angles in arithmetical progression. 



Horta, F. Lisb. A. 1 (1857) 713-. 



symbolic operators, theorems. Glaisher, 

 J. W. L. QJ. Mth. 15 (1878) 266-. 



Exponentials, representation of function. 01- 

 tramare, G. Sch. Nf. Gs. Vh. (1896) 50-. 



Fractional power of (-j--\ x' } . Center, W. 



Camb. and Dubl. Mth. J. 3 (1848) 163-. 

 Functional equations, replacement of arbitrary 

 constants by operative symbols. Tanner, 

 H. W. L. Mess. Mth. 7 (1878) 157- ; 8 (1879) 

 13. 



operations, certain. Pincherle, S. Bologna 

 Ac. Sc. Mm. 7 (1886) 393-. 



, groups. Levi-Civita, T. Mil. I. Lomb. 



Ed. 28 (1895) 458-, 864-. 

 , , and the inversion of definite integrals. 



Levi-Civita, T. Mil. I. Lomb. Ed. 28 (1895) 



529-, 565-. 

 Functions, determination by formal conditions. 



Schroder, E. Crelle J. Mth. 90 (1881) 189-. 

 , symbolic representations. Bronwin, B. 



Camb. and Dubl. Mth. J. 2 (1847) 134-. 

 General algorithms and iteration. Lemeray, . 



C. E. 126 (1898) 510- ; Par. S. Mth. Bll. 26 



(1898) 10-. 

 Hyperdistributives. Cockle, (Sir) J. Ph. Mg. 



43 (1872) 300-. 

 Integration problems. Rubini, R. G. Mt. 19 



(1881) 118-. 

 Iteration. Bourlet, C. C. E. 126 (1898) 583-. 



of functions. Aristov, I. I. Kazan S. Ps.- 

 Mth. Bll. 10 (1901) 14-, 85-; Fschr. Mth. 

 (1900) 403-. 



, the problem. Bourlet, C. Toul. Fac. Sc. 



A. 12 (1898) c, 12 pp. 

 , . Lemeray, . C. E. 128 (1899) 



278-, 380. 

 Iterative calculus, principles. Bottcher, . E. 



Prace Mt.-Fiz. 10 (1899-1900) 65-. 

 Laplace's transformation. Amaldi, U. Em. E. 



Ac. Line. Ed. 7 (1898) (Sem. 2) 117-. 

 Law of combination of operators. Campbell, 



J. E. [1897] L. Mth. S. P. 29 (1898) 14-. 

 Mathematical operations, especially restricted 



differentiation. Gruenewald, . D. Nf. Tbl. 



(*1868) 130-. 



Multiplication of functional distributive opera- 

 tions. Bortolotti, E. Em. E. Ac. Line. 



Ed. 7 (1898) (Sem. 1) 16-. 

 partial differential operators. Sylvester, 



J. J. Ph. Mg. 33 (1867) 48-. 

 Notation, "representative." Blissard, J. [1862] 



QJ. Mth. 6 (1863) 49-. 

 0, a certain differential, determinantal operator. 



Vivanti, G. Palermo Cir. Mt. Ed. 4 (1890) 



261-. 

 Operation on functions, definition [<f>n(x) for 



<f> (x) repeated n times, where n is fractional]. 



Appell, P. Par. S. Phlm. Bll. 3 (1879) 



166. 



52 



