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Results tagged with asymptotics
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user 18910
Asymptotic behavior of functions, asymptotic series and related topics
2
votes
1
answer
267
views
Asymptotic expansion of hypergeometric function ${}_3F_2$ for large parameters
I encountered the following hypergeometric function in my research: $${}_3F_2(2,1+n,1+n;1,2+n;z)$$ where $0<z<1$. I'm interested in its behavior for large $n$. Semilog plot suggests exponential incr …
- 907
3
votes
0
answers
581
views
Sum of binomial coefficients weighted by a lower incomplete regularized gamma function
The following summation turned up in the course of my research:
$$S_n=\sum_{k=0}^n {n \choose k}\lambda^k P(k,t)$$
where $P(k,t)=\frac{1}{\Gamma(k)}\int_{0}^t e^{-x}x^{k-1}dx$ is the lower incomplet …
- 907