Mittag-Leffler Polynomial
المؤلف:
Bateman, H
المصدر:
"The Polynomial of Mittag-Leffler." Proc. Nat. Acad. Sci. USA 26
الجزء والصفحة:
...
20-9-2019
1748
Mittag-Leffler Polynomial
Polynomials 
which form the associated Sheffer sequence for
 |
(1)
|
and have the generating function
 |
(2)
|
An explicit formula is given by
 |
(3)
|
where 
is a falling factorial, which can be summed in closed form in terms of the hypergeometric function, gamma function, and polygamma function. The binomial identity associated with the Sheffer sequence is
 |
(4)
|
The Mittag-Leffler polynomials satisfy the recurrence formula
![M_(n+1)(x)=1/2x[M_n(x+1)+2M_n(x)+M_n(x-1)].](http://mathworld.wolfram.com/images/equations/Mittag-LefflerPolynomial/NumberedEquation5.gif) |
(5)
|
The first few Mittag-Leffler polynomials are
The Mittag-Leffler polynomials 
are related to the Pidduck polynomials by
 |
(11)
|
(Roman 1984, p. 127).
REFERENCES:
Bateman, H. "The Polynomial of Mittag-Leffler." Proc. Nat. Acad. Sci. USA 26, 491-496, 1940.
Roman, S. "The Mittag-Leffler Polynomials." §4.1.6 in The Umbral Calculus. New York: Academic Press, pp. 75-78 and 127, 1984.
الاكثر قراءة في التفاضل و التكامل
اخر الاخبار
اخبار العتبة العباسية المقدسة
