A Treatise on the Calculus of Finite Differences |
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Page 1
... indefinitely dimi- nished . In the latter branch of analysis if we represent the inde- pendent variable by x , any dependent variable considered as a function of x is represented primarily indeed by ( x ) , but , when the rules of ...
... indefinitely dimi- nished . In the latter branch of analysis if we represent the inde- pendent variable by x , any dependent variable considered as a function of x is represented primarily indeed by ( x ) , but , when the rules of ...
Page 12
... indefinitely diminished . General theorems expressing relations between the successive values , successive differences , and successive differential coef- ficients of functions . 6. In the equation of definition △ U x = Ux + 1— U x we ...
... indefinitely diminished . General theorems expressing relations between the successive values , successive differences , and successive differential coef- ficients of functions . 6. In the equation of definition △ U x = Ux + 1— U x we ...
Page 65
... indefinitely increased . This definition leads us to distinguish between the con- vergency of a series and the convergency of the terms of a series . The successive terms of the series 1 1 1 1+ + + + 3 1 + & c . converge to the limit 0 ...
... indefinitely increased . This definition leads us to distinguish between the con- vergency of a series and the convergency of the terms of a series . The successive terms of the series 1 1 1 1+ + + + 3 1 + & c . converge to the limit 0 ...
Page 69
... indefinitely increased , to a limiting Ux + 1 Их value less or greater than unity . Let h be that limiting value ; and first let h be less than 1 , and let k be some positive quantity so small that h + k shall also be less than 1. Then ...
... indefinitely increased , to a limiting Ux + 1 Их value less or greater than unity . Let h be that limiting value ; and first let h be less than 1 , and let k be some positive quantity so small that h + k shall also be less than 1. Then ...
Page 71
... indefinitely increased , to the limit t . Accordingly therefore as t is less or greater than unity , the series is ... indefinite number of factors involved in the expression of the general term of the series . We proceed , therefore ...
... indefinitely increased , to the limit t . Accordingly therefore as t is less or greater than unity , the series is ... indefinite number of factors involved in the expression of the general term of the series . We proceed , therefore ...
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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
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