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In this way, we can construct the Stratonovich–Taylor–Hall (STH) schemes which are more ecient than those Stratonovich–Taylor (ST) schemes as they involve only the minimum numbers

214 –215], in which he gave a proof of the Rogers–Ramanujan identities (1.6), Ramanujan did provide a proof of (1.5), but he never proved in print anything else about R ( q ) :

The greater part of them are based on an implicit method, usually a classical Runge–Kutta (RK) method or a multistep RK method, in which the implicit relations are solved by

A case of particular interest is the one for which n grows faster than n: Rescaling the argument z appropriately the resulting asymptotic forms are described by elementary