How Do You Spell RESUMMATION?

Pronunciation: [ɹɪsəmˈe͡ɪʃən] (IPA)

The word "resummation" (/ˌriːsʌˈmeɪʃən/) describes the process of adding up or consolidating multiple things, typically in a mathematical or scientific context. Its spelling reflects the prefix "re-" indicating repetition or re-doing, plus the root word "summation" meaning addition. The doubled letter "m" signals a stressed syllable ("suMMA") followed by an unstressed one ("tion"). While not a commonly used term in everyday language, resummation plays a crucial role in many academic fields and technical applications.

RESUMMATION Meaning and Definition

1. Resummation is a mathematical technique used in various branches of science, particularly in theoretical physics and mathematics. It involves the process of summing an infinite number of terms in a series in order to obtain a more accurate result or to simplify the expression.

   In the context of theoretical physics, resummation is employed to deal with perturbative expansions. Perturbation theory is often utilized to solve complex problems in physics, but it can lead to convergent series that fail to provide accurate results when summed to a finite order. Resummation attempts to overcome this limitation by summing an infinite number of terms in the series to improve the precision of the solution.

   Resummation techniques are also employed in mathematics, particularly in the field of analytic combinatorics. In this context, resummation aims to obtain a closed-form expression for the generating function of a sequence. By analyzing the asymptotic behavior of the generating function and applying resummation techniques, mathematicians can obtain precise information about the growth rate and other properties of the corresponding sequence.

   Overall, resummation is a powerful tool for improving the accuracy and simplifying mathematical expressions by summing an infinite series of terms. It finds applications in a wide range of scientific disciplines, enabling researchers to obtain more precise and insightful results.

Etymology of RESUMMATION

The word "resummation" is derived from the combination of the prefix "re-" and the noun "summation".

The prefix "re-" comes from the Latin term "re-" which means "again" or "back". It is a common prefix used in English to indicate repetition or reoccurrence of an action.

The noun "summation" comes from Latin "summare" which means "to sum up" or "to total". It is derived from the Latin word "summa" meaning "the highest, the top" or "the essence". In English, "summation" refers to the process of adding up individual numbers or elements to achieve a total.

Therefore, "resummation" combines the notion of repeating or doing something again ("re-") with the process of totaling or adding up elements ("summation").