A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 74
... presented in another form . 1 For representing by ( x ) , and applying to each of the functions Их in ( A ) , the rule for indeterminate functions of the form we have lp ( x ) __ p ' ( x ) loc 1 $ ( x ) x Ux = φ ( 2 ) 1 x = x & ' ( x ) ...
... presented in another form . 1 For representing by ( x ) , and applying to each of the functions Их in ( A ) , the rule for indeterminate functions of the form we have lp ( x ) __ p ' ( x ) loc 1 $ ( x ) x Ux = φ ( 2 ) 1 x = x & ' ( x ) ...
Side 99
... presented in a form involving successive values , instead of successive differences , of the dependent variable ; for Au , can be expressed in terms Chap . II . Art . 10 . of Ux , Ux + 1 ... Ux + n • Equations of differences are said to ...
... presented in a form involving successive values , instead of successive differences , of the dependent variable ; for Au , can be expressed in terms Chap . II . Art . 10 . of Ux , Ux + 1 ... Ux + n • Equations of differences are said to ...
Side 115
... presented in the form A2 2 Uzen + A ̧Þ ( X ) Uz + n - 1 + 43 $ ( x ) $ ( x − 1 ) Un - 2 + & c . = X Ux + n − 1 a ....... ( 4 ) . Hence , to integrate them it is only necessary to 8-2 ART . 9. ] 115 EQUATIONS OF DIFFERENCES .
... presented in the form A2 2 Uzen + A ̧Þ ( X ) Uz + n - 1 + 43 $ ( x ) $ ( x − 1 ) Un - 2 + & c . = X Ux + n − 1 a ....... ( 4 ) . Hence , to integrate them it is only necessary to 8-2 ART . 9. ] 115 EQUATIONS OF DIFFERENCES .
Side 120
... - 1-1 U x = V x P Vx + 1 Vx + 2 Bv P Vx + 2 cach summation introducing an arbitrary constant . If we make p B2 - 12-1 = T2 P Vx + 1 Tx the above solution may be presented in the form X 120 [ CH . VII . EQUATIONS OF DIFFERENCES .
... - 1-1 U x = V x P Vx + 1 Vx + 2 Bv P Vx + 2 cach summation introducing an arbitrary constant . If we make p B2 - 12-1 = T2 P Vx + 1 Tx the above solution may be presented in the form X 120 [ CH . VII . EQUATIONS OF DIFFERENCES .
Side 121
George Boole. the above solution may be presented in the form X BxvxTx x = v . Σ ( TΣBAT ) . If X = 0 we have simply Ux = vx ( C + C1ΣTË ) . Fundamental Connexion with Differential Equations . 11. Equations of differences are connected ...
George Boole. the above solution may be presented in the form X BxvxTx x = v . Σ ( TΣBAT ) . If X = 0 we have simply Ux = vx ( C + C1ΣTË ) . Fundamental Connexion with Differential Equations . 11. Equations of differences are connected ...
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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
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