A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 6
... employ the notation x ( x - 1 ) ... ( x - m + 1 ) = x ( m ) doing which , we have Ax ( m ) = mx ( m . ( m - 1 ) Hence , ( - ) being also a factorial term , .. ( 1 ) , ( 2 ) . and generally A2x ( m ) ' = m ( m − 1 ) x ( m − 2 ) ...
... employ the notation x ( x - 1 ) ... ( x - m + 1 ) = x ( m ) doing which , we have Ax ( m ) = mx ( m . ( m - 1 ) Hence , ( - ) being also a factorial term , .. ( 1 ) , ( 2 ) . and generally A2x ( m ) ' = m ( m − 1 ) x ( m − 2 ) ...
Side 7
... Employing the most general form of factorials , we find - Auzux - 1 Ux - m + 1 = ( Ux + 1 — Ux - m + 1 ) × U2Ux - 1 ... A 1 UxUx + 1 Ux + m - 1 ... and in particular if u „ = ax + b , Au2Ux_1 ... Ux_m7 + 1 ... Их - m + 2 ( 7 ) , ( 8 ) ...
... Employing the most general form of factorials , we find - Auzux - 1 Ux - m + 1 = ( Ux + 1 — Ux - m + 1 ) × U2Ux - 1 ... A 1 UxUx + 1 Ux + m - 1 ... and in particular if u „ = ax + b , Au2Ux_1 ... Ux_m7 + 1 ... Их - m + 2 ( 7 ) , ( 8 ) ...
Side 12
George Boole. we shall find by proceeding as before , except in the employ- ing of A for A , where Ax = h , 2 Ax $ ( x ) = { $ ( x ) } + ( Δφ ( α ) ) x + Δη { ( △ 2 ‡ ( x ) \ x ( x − h ) ( Ax ) ) 1. 2 - + + & c .... ( 6 ) , ( Ax ) 3 ...
George Boole. we shall find by proceeding as before , except in the employ- ing of A for A , where Ax = h , 2 Ax $ ( x ) = { $ ( x ) } + ( Δφ ( α ) ) x + Δη { ( △ 2 ‡ ( x ) \ x ( x − h ) ( Ax ) ) 1. 2 - + + & c .... ( 6 ) , ( Ax ) 3 ...
Side 15
... kind of indices supposed admissible . Hence the distributive property of the symbol G , as virtually employed in the above example , supposes limitations which are not ART . 8. ] DIRECT THEOREMS OF FINITE DIFFERENCES . 15.
... kind of indices supposed admissible . Hence the distributive property of the symbol G , as virtually employed in the above example , supposes limitations which are not ART . 8. ] DIRECT THEOREMS OF FINITE DIFFERENCES . 15.
Side 24
... employed in the above investigation pro- ceeds upon the assumption that n is a positive integer . The very important case in which n = -1 will be considered in another chapter of this work . Ex . 5. To express da dru in terms of the ...
... employed in the above investigation pro- ceeds upon the assumption that n is a positive integer . The very important case in which n = -1 will be considered in another chapter of this work . Ex . 5. To express da dru in terms of the ...
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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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