A077946 | Expansion of \( \dfrac{1}{1 - x - 2x^2 - 2x^3} \) |
The number arises as a coefficient of \(x\) in the Taylor Series expansion of the function at \(x=0\). The coefficients listed up to 24491 are:
1, 1, 3, 7, 15, 35, 79, 179, 407, 923, 2095, 4755, 10791, 24491
This means that the function can be expressed as:
\(1 + x + 3x^2 + 7x^3 + 15x^4 + 35x^5 + \dots \)
The Taylor Series for any continuous function \( f(x)\)at a point \(x=a\) is given by the following expression:$$f(x)=f(a)+\frac{f'(a)}{1!} (x-a) + \frac{f''(a)}{a!} (x-a)^2+ \frac{f'''(a)}{3!} (x-a)^3 + \dots$$A Maclaurin Series is a Taylor Series where \(a=0\).
1, 1, 3, 7, 15, 35, 79, 179, 407, 923, 2095, 4755, 10791, 24491
This means that the function can be expressed as:
\(1 + x + 3x^2 + 7x^3 + 15x^4 + 35x^5 + \dots \)
The Taylor Series for any continuous function \( f(x)\)at a point \(x=a\) is given by the following expression:$$f(x)=f(a)+\frac{f'(a)}{1!} (x-a) + \frac{f''(a)}{a!} (x-a)^2+ \frac{f'''(a)}{3!} (x-a)^3 + \dots$$A Maclaurin Series is a Taylor Series where \(a=0\).
Here is a permalink that will display these results using SageMathCell. I have a later post about Taylor Series that I created on April 27th 2018.
REFURBISHED on Saturday November 26th 2022
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