Hypergeometric Series And Ramanujan Type Series For π

In this master thesis,we show how the Gaussian summation and the Ramanujan-type for 1/πseries be rewritten.In this paper we introduce a number of other Ramanujan-type series for 1/πbe derived in a recurrence way and show how the high-order recurrence formula is derived based on the first-order recurrence formula and use the the high-order recurrence formula to obtain more rapidly converging series for 1/π.