A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 14
... positive integer values of n whatever . 8. We proceed to demonstrate the same theorem by the method of generating functions . Definition . If ( t ) is capable of being developed in a series of powers of t , the general term of the ...
... positive integer values of n whatever . 8. We proceed to demonstrate the same theorem by the method of generating functions . Definition . If ( t ) is capable of being developed in a series of powers of t , the general term of the ...
Side 17
... positive indices . For , by the implied definition of the index m , AA " u = ( AA ... m times ) ( AA ... n times ) u { AA ... ( m + n ) times } u = m + n1 These are the primary laws of combination of the symbol A. It will be seen from ...
... positive indices . For , by the implied definition of the index m , AA " u = ( AA ... m times ) ( AA ... n times ) u { AA ... ( m + n ) times } u = m + n1 These are the primary laws of combination of the symbol A. It will be seen from ...
Side 22
... positive and integral powers of t , when such development is possible , may be expressed in the form d $ ( t ) = $ ( 0 ) + $ ( 1 ) 0.t + o 02 . جمع d do 1 . 2 d do ++ ( 1 ) 0 ° . 1.2.3 t3 + & c . d where po denotes what & tm becomes ...
... positive and integral powers of t , when such development is possible , may be expressed in the form d $ ( t ) = $ ( 0 ) + $ ( 1 ) 0.t + o 02 . جمع d do 1 . 2 d do ++ ( 1 ) 0 ° . 1.2.3 t3 + & c . d where po denotes what & tm becomes ...
Side 24
... positive integer . Then observing that $ ( 0 ) = 0 , d φ ( 2 ) 0m = " — ( e2 – 1 ) ” 0 ′′ - 0m = Ar0m , we have - ( et − 1 ) " = △ " 0 . t + A ” 02 . ts + A " 03 . + & c . 1.2 1.2.3 But A " 0 " is equal to 0 if m is less than n , and ...
... positive integer . Then observing that $ ( 0 ) = 0 , d φ ( 2 ) 0m = " — ( e2 – 1 ) ” 0 ′′ - 0m = Ar0m , we have - ( et − 1 ) " = △ " 0 . t + A ” 02 . ts + A " 03 . + & c . 1.2 1.2.3 But A " 0 " is equal to 0 if m is less than n , and ...
Side 47
... positive integer . When i = 0 we have m = 0 , and the corresponding term in ( 7 ) reduces to a constant . But when i is a positive integer , we have in the second member of ( 7 ) a pair of terms of the form € - which , on making C + CA ...
... positive integer . When i = 0 we have m = 0 , and the corresponding term in ( 7 ) reduces to a constant . But when i is a positive integer , we have in the second member of ( 7 ) a pair of terms of the form € - which , on making C + CA ...
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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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