Answer by timur for "Continuized" Taylor Series? $\sin(x)=\sum...
Here is a partial answer to some of the questions.In this book, page 217 (see also this thread), it was established that$$f(z)=\int_0^\infty\frac{z^tdt}{\Gamma(t+1)} = e^z+O(|z|^{-N}),$$for any integer...
View ArticleAnswer by Winther for "Continuized" Taylor Series? $\sin(x)=\sum...
In none of the cases you have put up is there a perfect equality. The functions you define are just approximately the same as the corresponding infinite series (it's easy to prove this; just select one...
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"Continuized" Taylor Series? $\sin(x)=\sum...
~~not trying to reinvent the Laplace transform, but just an exploration into these particular series and integrals~~Current answers don't fully address the 5 questions, so any new ideas or suggestions...
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