Inequalities for the Normal Integral including a New Continued Fraction
نویسنده
چکیده
for R(t) which is rapidly convergent for small values of t and which incidentally provides a new set of inequalities. The rapidity of convergence is compared with a series for R(t) and with the Laplace C.F. for R(t). This assessment is similar to recent work by Teichroew (1952) on the comparative rapidity of convergence of series ando.F.'s for the elementary function e?, hi (1 + x) and arc tan x. Lane (1944) has also considered the same sort of thing for interpolation, comparing Newton's series and Thiele's C.F. in the case of the function 2. We also prove and generalize a conjecture of Birnbaumf (1950) that for (^0,
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