Log expansions

mathelord

How Do I Find The Logarithmic Expansions Of Log[x],i Mean The Series Of Log[x].it Is Urgent

Homework Helper

mustafa

The series expansion of any function can be obtained by Taylor's series expansion:
f(x)=f(a)+(x-a)f'(a)+(x-a)^2f"(a)/2!+(x-a)^3f"'(a)/3!+...

Using the above formula, any function can be expanded in terms of powers of (x-a), provided that all derivatives of f(x) are defined at x=a.

Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.

Homework Helper

lurflurf

Homework Helper
mustafa said:
Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.
I think you mean log x cannot be expanded about zero in a series of nonnegative powers.

MaxwellPhill

example can be done via the log(1+x) series |x|<1

x-x^2/2+x^3/3....

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving