bio  website  math.purdue.edu/~eremenko 

location  United States  
age  59  
visits  member for  1 year, 8 months 
seen  3 hours ago  
stats  profile views  6,737 
Math Professor
2h

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Find the Range of Function
Same question with $\mathbb{R}^m$ seems to be interesting too. 
2h

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Find the Range of Function
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3h

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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 
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What areas of pure mathematics research are best for a postPhD transition to industry?
Yes, of course, I do not forget. 
Apr 10 
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Solving Bessellike 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 
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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 
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Recognize this sum
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Apr 10 
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Recognize this sum
The reference you gave shows relation to Bessel functions when $\alpha=1$ only. 
Apr 10 
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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 
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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 
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Recognize this sum
Without the factorial, this would be the MittagLeffler function. Dividing on that factorial corresponds to a kind of Laplace transform. I don't think that Laplace transform of a MittagLeffler function is a "known function". 
Apr 9 
revised 
Algebraic Geometry for nonmathematician
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Apr 9 
answered  Algebraic Geometry for nonmathematician 
Apr 9 
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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 
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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 