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Roger S.
Roger S.
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Approximating $\prod_{i=1}^{n-1} (1-anai)$ for large $n$

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$$f(n) = \prod_{i=1}^{n-1} (1-ai)$

Here, $a \geq 0$ and $(a*n) < 1$$(a*i) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

Approximating $\prod_{i=1}^{n-1} (1-an)$ for large $n$

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$

Here, $a \geq 0$ and $(a*n) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

Approximating $\prod_{i=1}^{n-1} (1-ai)$ for large $n$

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-ai)$

Here, $a \geq 0$ and $(a*i) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

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Roger S.
Roger S.
  • 67
  • 4

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$

ForHere, $a \geq 0$ and $(a*n) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$

For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$

Here, $a \geq 0$ and $(a*n) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?

Source Link
Roger S.
Roger S.
  • 67
  • 4

Approximating $\prod_{i=1}^{n-1} (1-an)$ for large $n$

I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-an)$

For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?