incomplete gamma function Γ ( a , x ) for a >1 and x >; a ; these approximations become particularly useful for a > 1, and hence for χ 2 - tests in high-statistics experiments with many degrees of freedom, where they are more efficient than the standard method of continued ...
according to a recipe first described by Matiyasevich for the Riemann xi function. We show that these approximations converge to the true L-function and point out the role of an equidistributional notion in ensuring the approximation is well-defined, and along the way we demonstrate error formula...
we must take into accounteachof thenterms in the sum (1.17) (they all contribute). As can be seen from (1.17), this means that we need precise uniform asymptotics for\gamma ({\tilde{a}},z)as bothz \rightarrow + \inftyand{\tilde{a}} \rightarrow + \inftyat various...
Ramanujan’s approximation to the exponential function is reexamined with the help of Perron’s saddle-point method. This allows for a wide generalization that includes the results of Buckholtz, and where all the asymptotic expansion coefficients may be given in closed form. Ramanujan’s approximation...
U. Blahak. Efficient approximation of the incomplete gamma function for use in cloud model applications. Geoscientific Model Development, 3(2):329-336, 2010.U. Blahak, "Efficient approximation of the incomplete gamma function for use in cloud model applications." Geoscientific Model Development ...
Boudjelkha M T,Chaudhry M A.On the approximation of a generalizedincomplete gamma function arising in heat conduction problems[J].Math Anal Appl,2000,248(2):509-519.On the Approximation of a Generalized Incomplete Gamma Function Arising in Heat Conduction Problems[J] . M.T. Boudjelkha,M....
Journal of Statistical Computation and SimulationThe incomplete Gamma function and Ramanujan’s rational approximation to ex - Marsaglia - 1986 () Citation Context ...as x →∞ m(x) = x − 1 8 184 + + 3 405x 25515x2 + o(x−2 ) as x →∞. Remark 4.3 Choi ([6]) found the...
First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general...
Several asymptotic expansions are given for the generalized incomplete gamma function Γ(α,x;b)=∫∞xtα1etb/tdt, x>0, Reb≥0, b≠0, as x tends to infinity, where the real parameter α is allowed to take negative values. In the case b=iω, ω>0, we obtain the expansions of ...
A note on the approximation of the incomplete gamma function by a method of G. Meinardusdoi:10.1016/0893-9659(88)90184-XGuido WalzApplied Mathematics Letters