Taylor Series for log ⁡ ( x )Does anyone know a closed form expression for...

boloman0z

boloman0z

Answered

2022-06-25

Taylor Series for log ( x )
Does anyone know a closed form expression for the Taylor series of the function f ( x ) = log ( x ) where log ( x ) denotes the natural logarithm function?

Answer & Explanation

Xzavier Shelton

Xzavier Shelton

Expert

2022-06-26Added 26 answers

log ( 1 x ) = x + x 2 2 + x 3 3 + ( | x | < 1 )
There is no expansion around x = 1 because the log is singular at 0.
Craig Mendoza

Craig Mendoza

Expert

2022-06-27Added 6 answers

For x R satisfying 0 < x < 2
f ( x ) = ln ( x ) = ( x 1 ) 1 2 ( x 1 ) 2 + 1 3 ( x 1 ) 3 1 4 ( x 1 ) 4 +
f ( x ) = n = 1 [ ( 1 ) n + 1 n ( x 1 ) n ]

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?