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bio website math.purdue.edu/~eremenko
location United States
age 59
visits member for 1 year, 8 months
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Math Professor

2h
comment Find the Range of Function
Same question with $\mathbb{R}^m$ seems to be interesting too.
2h
revised Find the Range of Function
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3h
comment Question about conjugate points
I added a very explicit picture.
3h
revised Question about conjugate points
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3h
answered Question about conjugate points
Apr
12
comment What areas of pure mathematics research are best for a post-PhD transition to industry?
Yes, of course, I do not forget.
Apr
10
comment Solving Bessel-like equation by using Bessel Kernel
This formula can be produced by the "method of variation of constant" explained in every undergraduate ODE text.
Apr
10
comment Recognize this sum
For the definition of order and type, see any book which has "Entire functions" in the title, the best one is Levin, Lectures on entire functions, or another book of the same author.
Apr
10
awarded  Nice Answer
Apr
10
revised Recognize this sum
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Apr
10
comment Recognize this sum
The reference you gave shows relation to Bessel functions when $\alpha=1$ only.
Apr
10
comment Recognize this sum
If $\alpha<0$ my arguments are not valid, but then all depends on the arithmetic nature of alpha, how close its multiples can approximate integers. Still does not look like anything familiar.
Apr
10
answered Recognize this sum
Apr
10
comment Recognize this sum
When $\alpha>1$ is irrational, I can prove that it does not satisfy any linear ODE with polynomial coefficients. So it is unlikely to be related to Bessel or to any special function.
Apr
10
comment Recognize this sum
Without the factorial, this would be the Mittag-Leffler function. Dividing on that factorial corresponds to a kind of Laplace transform. I don't think that Laplace transform of a Mittag-Leffler function is a "known function".
Apr
9
revised Algebraic Geometry for non-mathematician
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Apr
9
answered Algebraic Geometry for non-mathematician
Apr
9
comment Looking for paper: The Cauchy integral by M. Privalov
Loic Teyssier: reload once or twice, and click on the book cover. You need to install a djview reader too.It works most of the time.
Apr
9
comment Looking for paper: The Cauchy integral by M. Privalov
Thanks for the web site.
Apr
9
answered Looking for paper: The Cauchy integral by M. Privalov