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

Повторяя¹ это рассуждение, мы получим² тот же³ результат для функции  f (x).

By repeating this argument, we obtain the same result for the function  f (x).

Notes

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. ^

(6)

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. ^

(7)

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. ^