  Physically relevant field-theoretic quantities are usually derived from
perturbation techniques. These quantities are solved in the form of an
asymptotic series in powers of small perturbation parameters related to the
physical system, and calculating higher powers typically results in a higher
amount of computational complexity. Such divergent expansions were handled
using hyper-geometric functions, continued functions, and Borel-Leroy
transforms. Hypergeometric functions are expanded as series, and a rough
estimate of next-order information is predicted using information from known
orders. Continued functions are used for the resummation of these series. The
effective nature of extrapolation using such functions is illustrated by taking
different examples in field theories. In the vicinity of second-order phase
transitions, critical exponents are the most interesting numerical quantities
corresponding to a wide range of physical systems. Using the techniques
mentioned in this work, precise estimates are obtained for these critical
exponents in {\phi}^4 and {\phi}^3 field models.
