Umbral Calculus
The study of certain properties of Sylvester 
from the word ``umbra'' (meaning ``shadow'' in Latin), and reflects the fact that for many types of identities involvingsequences of polynomials with Powers 
, ``shadow'' identities are obtained when the polynomials arechanged to discrete values and the exponent in is changed to the Pochhammer Symbol 
.
For example, Newton's Forward Difference Formula written in the form
 | (1) |
looks suspiciously like a finite analog of the Taylor Series expansion | (2) |
is the Differential Operator. Similarly, the Chu-Vandermonde Identity | (3) |
a Binomial Coefficient, looks suspiciously like an analog of the Binomial Theorem | (4) |
References
Roman, S. and Rota, G.-C. ``The Umbral Calculus.'' Adv. Math. 27, 95-188, 1978. Roman, S. The Umbral Calculus. New York: Academic Press, 1984.
- Minus or Plus
- Minus Sign
- Minute
- Miquel Circles
- Miquel Equation
- Miquel Point
- Miquel's Theorem
- Miquel Triangle
- Mira Fractal
- Mirimanoff's Congruence
- Mirror Image
- Mirror Plane
- Misère Form
- Mitchell Index
- Miter Surface
- Mittag-Leffler Function
- Mittenpunkt
- Mixed Partial Derivative
- Mixed Strategy
- Mixed Tensor
- Mnemonic
- Mock Theta Function
- Mod
- Mode
- Model Completion