A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 15
... infinite variety of answers according to the extent of the development and the kind of indices supposed admissible . Hence the distributive property of the symbol G , as virtually employed in the above example , supposes limitations ...
... infinite variety of answers according to the extent of the development and the kind of indices supposed admissible . Hence the distributive property of the symbol G , as virtually employed in the above example , supposes limitations ...
Side 28
... infinite . Thus the form of the function - the species of the curve - must be assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of assumption is best . If for instance these ...
... infinite . Thus the form of the function - the species of the curve - must be assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of assumption is best . If for instance these ...
Side 40
... infinite at or within the limits , an appropriate transformation will be needed . πT Ex . 2. Required an approximate value of [ * log sin ede . 0 The function log sin @ becoming infinite at the lower limit , we have , on integrating by ...
... infinite at or within the limits , an appropriate transformation will be needed . πT Ex . 2. Required an approximate value of [ * log sin ede . 0 The function log sin @ becoming infinite at the lower limit , we have , on integrating by ...
Side 65
... infinite with n . On the other hand , the geometrical series 1 1 1 1 1+ + + + + & c . 2 4 8 16 is convergent both as respects its terms and as respects the sum of its terms . 2. Two cases present themselves . 1st . That in which the ...
... infinite with n . On the other hand , the geometrical series 1 1 1 1 1+ + + + + & c . 2 4 8 16 is convergent both as respects its terms and as respects the sum of its terms . 2. Two cases present themselves . 1st . That in which the ...
Side 67
... infinite . a For since ( x ) diminishes from xa to x = a + 1 , and again from x = a + 1 to x = a + 2 , & c . , we have ra + 1 fa α ra + 2 4 $ ( x ) dx < $ ( a ) , [ ** p ( x ) dx < $ ( a + 1 ) , a + 1 and so on , ad inf . Adding these ...
... infinite . a For since ( x ) diminishes from xa to x = a + 1 , and again from x = a + 1 to x = a + 2 , & c . , we have ra + 1 fa α ra + 2 4 $ ( x ) dx < $ ( a ) , [ ** p ( x ) dx < $ ( a + 1 ) , a + 1 and so on , ad inf . Adding these ...
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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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