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| In mathematics, the '''Mahler polynomials''' ''g''<sub>''n''</sub>(''x'') are polynomials introduced by {{harvs|txt|last=Mahler|year=1930|authorlink=Kurt Mahler}} in his work on the zeros of the [[incomplete gamma function]].
| | I'm Archer (27) from Vorbasse, Denmark. <br>I'm learning Swedish literature at a local university and I'm just about to graduate.<br>I have a part time job in a college.<br><br>My weblog ... [http://www.amazon.com/Honey-Its-Miraculous-Healing-Powers-ebook/dp/B00MCIGCWI/ The Health Benefits and Applications of Honey] |
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| Mahler polynomials are given by the [[generating function]]
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| :<math>\displaystyle \sum g_n(x)t^n/n! = \exp(x(1+t-e^t)) </math>
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| Mahler polynomials can be given as the [[Sheffer sequence]] for the functional inverse of 1+''t''–''e''<sup>''t''</sup> {{harv|Roman|1984|loc=4.9}}.
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| The first few examples are {{OEIS|A008299}}
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| :<math>g_0=1;</math>
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| :<math>g_1=0;</math>
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| :<math>g_2=-x;</math>
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| :<math>g_3=-x;</math>
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| :<math>g_4=-x+3x^2;</math>
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| :<math>g_5=-x+10x^2;</math>
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| :<math>g_6=-x+25x^-15x^3;</math>
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| :<math>g_7=-x+56x^2-105x^3;</math>
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| :<math>g_8=-x+119x^2-490x^3+105x^4;</math>
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| ==References==
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| *{{Citation | last1=Mahler | first1=Kurt | title=Über die Nullstellen der unvollständigen Gammafunktionen. | language=German | jfm=56.0310.01 | year=1930 | journal=Rendiconti Palermo | volume=54 | pages=1–41}}
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| *{{Citation | last1=Roman | first1=Steven | title=The umbral calculus | url=http://books.google.com/books?id=JpHjkhFLfpgC | publisher=Academic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=1984 | volume=111}} Reprinted by Dover, 2005
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| [[Category:Polynomials]]
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Latest revision as of 07:50, 10 May 2014
I'm Archer (27) from Vorbasse, Denmark.
I'm learning Swedish literature at a local university and I'm just about to graduate.
I have a part time job in a college.
My weblog ... The Health Benefits and Applications of Honey