Principal Part

The principal part at of a function

is the portion of the Laurent series consisting of terms with negative degree. That is,

is the principal part of at . has an essential singularity at, if and only if the principal part is an infinite sum.

Other articles related to "principal part, principal parts":

Laurent Series - Principal Part - Multiplication
... Two Laurent series with only finitely many negative terms can be multiplied algebraically, the sums are all finite geometrically, these have poles at c, and inner radius of convergence 0, so they both converge on an overlapping annulus ... Thus when defining formal Laurent series, one requires Laurent series with only finitely many negative terms. ...
Principal Part - Other Definitions - Distribution Theory
... The term principal part is also used for certain kinds of distributions having a singular support at a single point ...
Ri-verbs - Overview
... peculiar thing about the ri-verbs is that they are written with an e in the second principal part (first person singular past indicative mood), even ... The principal parts of the ri-verbs are as following First principal part Second principal part Third principal part Infinitive First person singular past tense indicative mood Past participle Að snúa ("to ...
Principal Parts - By Language - Spanish
... verbs are traditionally held to have only one principal part, the infinitive, by which one can classify the verb into one of three conjugation paradigms (according ... the conjugation could be regularized by adding another principal part to vowel-alternating verbs, which shows the alternation ... singular, present tense, indicative mood form (hiero) as a principal part, and noting that the diphthong appears only when that syllable is stressed, the conjugation of herir becomes completely predictable ...
Principal Parts - By Language - Icelandic - Ri-verbs
... Icelandic Ri-verbs have the following principal parts First principal part Second principal part Third principal part Infinitive First person singular past tense indicative mood Past participle Að snúa ("to turn ... possible to make the past subjunctive mood (þótt ég sneri, "though I turned") from the second principal part (ég sneri, "I turned") ...

Famous quotes containing the words part and/or principal:

    In writing these Tales ... at long intervals, I have kept the book-unity always in mind ... with reference to its effect as part of a whole.
    Edgar Allan Poe (1809–1849)

    I would urge that the yeast of education is the idea of excellence, and the idea of excellence comprises as many forms as there are individuals, each of whom develops his own image of excellence. The school must have as one of its principal functions the nurturing of images of excellence.
    Jerome S. Bruner (20th century)