A Treatise on the Calculus of Finite Differences |
From inside the book
Results 1-5 of 18
Page 6
... involved is called a factorial term . For the particular kind of factorials illustrated in the above example it is com- mon to employ the notation x ( x - 1 ) ... ( x - m + 1 ) = x ( m ) doing which , we have Ax ( m ) = mx ( m . ( m - 1 ) ...
... involved is called a factorial term . For the particular kind of factorials illustrated in the above example it is com- mon to employ the notation x ( x - 1 ) ... ( x - m + 1 ) = x ( m ) doing which , we have Ax ( m ) = mx ( m . ( m - 1 ) ...
Page 16
... involved . In addition to the symbol A , we shall introduce a symbol D to denote the ope- ration of giving to x in a proposed subject function the incre- ment unity ; -its definition being Dux = Ux + 1 Laws and Relations of the symbols ...
... involved . In addition to the symbol A , we shall introduce a symbol D to denote the ope- ration of giving to x in a proposed subject function the incre- ment unity ; -its definition being Dux = Ux + 1 Laws and Relations of the symbols ...
Page 68
... involved in the demonstration of the final system of criteria referred to in Art . 3 . Ex . 1. The geometrical series 1 + h + h2 + h3 + & c . ad inf . is convergent if h < 1 , divergent if h х 1 . The general term is h " , the value of ...
... involved in the demonstration of the final system of criteria referred to in Art . 3 . Ex . 1. The geometrical series 1 + h + h2 + h3 + & c . ad inf . is convergent if h < 1 , divergent if h х 1 . The general term is h " , the value of ...
Page 71
... involved in the expression of the general term of the series . We proceed , therefore , to establish the supplemental criteria referred to in Art . 3 . Supplemental Criteria . 6. Let the series under consideration be Wa + Wa + 1 + Wa + ...
... involved in the expression of the general term of the series . We proceed , therefore , to establish the supplemental criteria referred to in Art . 3 . Supplemental Criteria . 6. Let the series under consideration be Wa + Wa + 1 + Wa + ...
Page 73
... involved in the succeeding tests , ad inf . , are now obvious . Practically , we are directed to construct the successive functions , 1 1 1 7 7 7 7 Их Xux 2 loc xlx ux lx xlxlxu " & c . ..... ( A ) , and the first of these which tends ...
... involved in the succeeding tests , ad inf . , are now obvious . Practically , we are directed to construct the successive functions , 1 1 1 7 7 7 7 Их Xux 2 loc xlx ux lx xlxlxu " & c . ..... ( A ) , and the first of these which tends ...
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.