A Treatise on the Calculus of Finite Differences |
From inside the book
Results 1-5 of 25
Page 5
... rational and integral function of x of the degree n - 1 . Re- peating the process , we have n - 2 -8 = an ( n − 1 ) x2 → 2 + С1x2¬3 + C2x22 + & c . , a rational and integral function of the degree n - 2 ; and so on . Finally we shall ...
... rational and integral function of x of the degree n - 1 . Re- peating the process , we have n - 2 -8 = an ( n − 1 ) x2 → 2 + С1x2¬3 + C2x22 + & c . , a rational and integral function of the degree n - 2 ; and so on . Finally we shall ...
Page 11
... rational and integral function of x of the mth degree , in a series of factorials . 1st . Assume ... ......... ( 1 ) . ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) The legitimacy of this form is evident , for it represents a rational ...
... rational and integral function of x of the mth degree , in a series of factorials . 1st . Assume ... ......... ( 1 ) . ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) The legitimacy of this form is evident , for it represents a rational ...
Page 28
... rational and integral function of x , and to determine the coefficients by the given conditions . This assumption rests upon the supposition ( a supposition however actually verified in the case of all tabulated func- tions ) that the ...
... rational and integral function of x , and to determine the coefficients by the given conditions . This assumption rests upon the supposition ( a supposition however actually verified in the case of all tabulated func- tions ) that the ...
Page 29
... rational and integral . Of course it is supposed that the value of x for which that of the function is required is not very remote from those , or from some of those , values for which the values of the func- tion are given . The same ...
... rational and integral . Of course it is supposed that the value of x for which that of the function is required is not very remote from those , or from some of those , values for which the values of the func- tion are given . The same ...
Page 30
... rational and integral and of the degree n - 1 , we have A " u = 0 , and therefore A " u , = 0 . Hence x ( x - 1 ) u2 = u2 + x △ u2 + A3u ... 1.2 + x ( x − 1 ) ... ( x − n + 2 ) - 1.2 ... ( n - 1 ) the expression required . It will be ...
... rational and integral and of the degree n - 1 , we have A " u = 0 , and therefore A " u , = 0 . Hence x ( x - 1 ) u2 = u2 + x △ u2 + A3u ... 1.2 + x ( x − 1 ) ... ( x − n + 2 ) - 1.2 ... ( n - 1 ) the expression required . It will be ...
Other editions - View all
Common terms and phrases
A₁ A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ c₂ Calculus of Finite Cambridge CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive CONIC SECTIONS convergent Crown 8vo curve deduce denoted determine Differential Calculus differential equation divergent English Notes equation of differences expression Fcap Fellow of St Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral John's College limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates P. G. TAIT particular value periodical function rational and integral reduced result Schools second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux+1 Ux+2 v₂ Vx+1 Vx+2 whence Их
Popular passages
Page 2 - FROST.— The First Three Sections of Newton's Principia. With Notes and Problems in illustration of the subject. By PERCIVAL FROST, MA late Fellow of St. John's College, Cambridge, and Mathematical Lecturer of Jesus College. Crown 8vo. cloth, 10s.
Page 6 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 2 - Scouring of the White Horse. Or, the Long Vacation Ramble of a London Clerk. By the Author of
Page 5 - The fitness of Holy Scripture for Unfolding the Spiritual Life of Man : Christ the Desire of all Nations ; or, the Unconscious Prophecies of Heathendom.
Page 15 - JW COLENSO, DD Bishop of Natal. The Colony of Natal. A Journal of Visitation. With a Map and Illustrations.
Page 1 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Page 5 - SPECTATOR. 6. Alexandria and Her Schools. Being Four Lectures delivered at the Philosophical Institution, Edinburgh. With a Preface. Crown Svo. cloth, 5*. " A series of brilliant biographical and literary sketches, interspersed with comments of the closest modern, or rather universal application
Page 4 - THRUPP.— Antient Jerusalem : a New Investigation into the History, Topography, and Plan of the City, Environs, and Temple.
Page 5 - Village Sermons. By a NORTHAMPTONSHIRE RECTOR. With a Preface on the Inspiration of Holy Scripture. Crown 8vo. 6s. Vittoria Colonna. — Life and Poems. By MRS. HENRY ROSCOE. Crown 8vo. 9s. Volunteer's Scrap Book. By the Author of "The Cambridge Scrap Book.