Chu, Inversion techniques and combinatorial identities--strange evaluations of hyper geometric series
, Pure Math.
Since Motomura (1932) developed the geometric series
model to describe the structure of an aquatic community, ecologists have built many models to fit species-abundance data derived from communities or collections.
It covers functions and change, rate of change; the derivative, short-cuts to differentiation, using the derivative, accumulated change; the definite integral, anti-derivatives and applications, probability, functions of several variables, mathematical modeling using differential equations, and geometric series
m]) is a geometric series
with first term 1 and common ratio r[[omega].
With M0 and MC it can be assumed that cosmic thermal energy density, matter energy density and the critical energy density are in geometric series
and the geometric ratio is 1 + 1n ([M.
One can use intuition alone or calculus and polar co-ordinates, but herein we offer a solution we have not seen presented elsewhere using the sum of a geometric series
applied in an unexpected way.
The addition of a Trapezoid (TRPC) and Radius (RDIC) Shape complete the compact Architectural Sconce Geometric Series
, and the LMC-30 (pictured) delivers a new powerful addition to the popular Laredo Series.
test] < 10) and only the Geometric series
model (Geoser) had a low octave test statistic ([oc.
This is easily proven by using an infinite geometric series
Zeilberger, Hyper geometric series
acceleration via the WZ method, Electron.
Blank Frank (all works 2009), for example, is a simple arrangement of two lightly painted kidney or lung shapes (an umbilical appendage growing from one) hovering over an inverted dark blue mound; floating to the left of these forms, a more geometric series
of brushy lines punctuates the otherwise anemic field.
Nowadays, the geometric series
play a key role in digital number system, for example, converting a base-2 number into a base-10 number.