Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 9
... of Analysis in the Transactions of the British Association ; and to two papers by Mr Great- heed in the Cambridge Mathematical Journal , Vol . 1 . SECT . 1. Functions of One Variable . ( 1 IL Successive Differentiation.
... of Analysis in the Transactions of the British Association ; and to two papers by Mr Great- heed in the Cambridge Mathematical Journal , Vol . 1 . SECT . 1. Functions of One Variable . ( 1 IL Successive Differentiation.
Сторінка 10
D. F. Gregory. SECT . 1. Functions of One Variable . ( 1 ) u = x " ; d'u dx = n ( n − 1 ) ... ...... . ( n − r + 1 ) x ” – ” . - ( 2 ) d'u dx u = ( a + bx ) " ; = n ( n − 1 ) ...... ( n − r + 1 ) b ' ( a + bx ) " ~ " ...
D. F. Gregory. SECT . 1. Functions of One Variable . ( 1 ) u = x " ; d'u dx = n ( n − 1 ) ... ...... . ( n − r + 1 ) x ” – ” . - ( 2 ) d'u dx u = ( a + bx ) " ; = n ( n − 1 ) ...... ( n − r + 1 ) b ' ( a + bx ) " ~ " ...
Сторінка 21
... 1 ) • + { 3 ′ − ( " + 1 ) 2 ′ + ( e + 1 ) ′ + 1 • Mémoires de l'Académie , 1777 , p . 108 . 1.2 ( r + 1 ) ~ 1 ' } e ( r − 8 ) • + & c . ] SECT . 2 . Functions of Two or more Variables SUCCESSIVE 21 DIFFERENTIATION .
... 1 ) • + { 3 ′ − ( " + 1 ) 2 ′ + ( e + 1 ) ′ + 1 • Mémoires de l'Académie , 1777 , p . 108 . 1.2 ( r + 1 ) ~ 1 ' } e ( r − 8 ) • + & c . ] SECT . 2 . Functions of Two or more Variables SUCCESSIVE 21 DIFFERENTIATION .
Сторінка 22
D. F. Gregory. SECT . 2 . Functions of Two or more Variables . If u be a function of two variables x and y , Ex . ( 1 ) dr + s u dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy ...
D. F. Gregory. SECT . 2 . Functions of Two or more Variables . If u be a function of two variables x and y , Ex . ( 1 ) dr + s u dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy ...
Сторінка 27
... x " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT SUCCESSIVE DIFFERENTIATION . 27.
... x " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT SUCCESSIVE DIFFERENTIATION . 27.
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