A. J. Lohwater's Russian-English Dictionary of the Mathematical Sciences

1.	Adverbial participle of повторить (to repeat); the translation of повторяя could have been rendered by "Repeating" or "If we repeat," to suit the taste of the translator. ↑
2.	Perfective form, and the future "we shall obtain" has the same sense, in the context, as "we obtain." ↑
3.	Note the pair тот же under тот or under же in the dictionary. ↑

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Распределение, задаваемое¹ функцией плотности² s_n(x) или функцией распределения² S_n(x) известно под названием распределения Стьюдента или t-распределения; оно было впервые использовано³ в одной важной статистической проблеме В. Госсетом, писавшим⁴ под псевдонимом «Стьюдент» (Student).

⁵

The distribution defined by the frequency function s_n(x) or the distribution function S_n(x) is known under the name of Student's distribution or the t-distribution; it was first used in an important statistical problem by W. Gosset, writing under the pseudonym of "Student."

Notes

1.	Present passive participle задаваемый of задавать (to define, etc.). ↑
2.	Cf. note 5 under example 2 of this section. ↑
3.	Short form of the participle использованный; with было the verb is passive. ↑
4.	The past active participle писавший of писать (to write); it may also be rendered as "who wrote" or "who was writing," the latter expressing literally the imperfective aspect of the verb. ↑
5.	When a Western surname is introduced into Russian for the first time, the original spelling in the Roman alphabet used sometimes to follow the transliteration into Russian; this is rarely done today. ↑

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Примеры § 1 показывают, что ряд может быть сходящимся,¹ не будучи² абсолютно сходящимся.¹

The examples of § 1 show that a series can be convergent without being absolutely convergent.

Notes

1.	Instrumental case of the predicate following the simple past or simple future of быть. ↑
2.	Adverbial participle of быть. ↑

Some Special Verbs

Examples of a number of auxiliary verbs and forms, such as must, can, etc., will be given in this section. Please refer to the section concerning modals in The Verb for further discussion.

1. Если скоростью частицы нельзя пренебречь по сравнению со скоростью света c или энергией её нельзя пренебречь по сравнению с энергией покоящейся массы, то необходимо пользоваться формулой λ_D = ... → If the velocity of the particle is not negligible compared to the velocity of light, c, or if the energy is not negligible compared to the rest mass energy, then it is necessary to use the formula λ_D = ... (Literally, If one must not, or cannot, neglect the velocity of the particle in comparison to the velocity of light, c, or if one must not neglect the energy, etc.)

The English words "must," "ought to," and "should" may also be rendered by следует followed by the infinitive; the past is следовало бы (should have, ought to have); for example

2. Следует быть острожным при использовании этой формулы. → One must be careful in using this formula.

3. Вам следовало бы исключить сначала A, затем B. → You should have eliminated A first, and then B.

Note. Следует may also have its usual meaning "follows," for example

4. Из (2) следует, что ... → It follows from (2) that ...

5. Самодуальному тензору G^ρσ можно сопоставить симметрический спинор второго ранга g_rs. → With a self-dual tensor G^ρσ one can associate a symmetric spinor g_rs of rank two. (Or: It is possible to associate with a self-dual tensor G^ρσ a symmetric spinor g_rs of rank two.)

6. Для заданного ε можно найти такое δ, что¹ |I₁| < ε/3 для всех значений n; зафиксировав² это значение δ, можно найти такое n

₀ = n₀(δ), что³ |I₂| < ε/3 и |I₃| < ε/3 при n > n₀. → For given ε, we can find δ such that |I₁| < ε/3 for all values of n; having fixed δ, we can find n₀ = n₀(δ) such that |I₂| < ε/3 and |I₃| < ε/3 for n > n₀.

  Notes