a b s t r a c tInspired by a method used by Bellard in 1997, we establish a trigonometric expansion for the function arctan a x−1 , and then utilize this expansion to derive numerous BBP-type formulae that converge, in most cases, to well-known irrational constants.
Several transformation and summation formulae for nonterminating basic hypergeometric series are established through the modified Abel lemma on summation by parts.
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