527formf - 642:527 FORMULA SHEET FOR FINAL EXAM FALL 2009...

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Unformatted text preview: 642:527 FORMULA SHEET FOR FINAL EXAM FALL 2009 Taylor series (with radii of convergence given): 1 1 x = 1 + x + x 2 + = summationdisplay x n , | x | < 1 e x = 1 + x + x 2 2! + x 3 3! + = summationdisplay x n n ! , | x | < cos x = 1 x 2 2! + x 4 4! = summationdisplay ( 1) n x 2 n (2 n )! , | x | < sin x = x x 3 3! + x 5 5! = summationdisplay ( 1) n x 2 n +1 (2 n + 1)! , | x | < The Gamma function. For x > 0, ( x ) = integraltext t x 1 e t d t . If x is not 0 or a negative integer, ( x + 1) = x ( x ). If n is a non-negative integer, ( n + 1) = n !. (1 / 2) = . The Method of Frobenioussolution forms: y 1 ( x ) = x r summationdisplay n =0 a n x n (= y 2 ( x ) ?), y 2 ( x ) = y 1 ( x )(ln x ) + x r 1 summationdisplay n =1 b n x n , y 2 ( x ) = Cy 1 ( x )(ln x ) + x r 2 summationdisplay n =0 b n x n ....
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This note was uploaded on 12/15/2009 for the course MATH 527 taught by Professor Staff during the Fall '08 term at Rutgers.

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527formf - 642:527 FORMULA SHEET FOR FINAL EXAM FALL 2009...

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