Q (a,z )=[GAMMA](a,z )/r(a) is the regularized incomplete gamma function
and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], is the incomplete gamma function
, and [GAMMA](a) is Euler gamma function.
Therefore this work proposes a unified non-linear interpretation for thermal analysis data based on the search of parameters E, A with non-linear minimization using the incomplete gamma function
to evaluate p(x).
where [GAMMA](*,*) is the incomplete gamma function
Therefore, using the formula for incomplete Gamma function
, which is given as
where all the input variables are now explicitly listed in the arguments of the ALDA function, and [GAMMA]F(x, y) denotes the incomplete Gamma function
1959, Some elementary inequalities relating to the Gamma and incomplete Gamma function
In this paper, we present first some properties of [tau]-hypergeometric function and the hypergeometric confluent function of the second kind and we also define a generalized form of the incomplete gamma function
and its complementary.
As a general example, modified expansions for confluent hypergeometric functions are considered in Section 3, and as particular cases expansions for the incomplete gamma function
[GAMMA](a, z) and the modified Bessel function [K.
Rudert, Tables of the Incomplete Gamma Function
Ratio, Justus von Liebig Verlag, Darmstadt, Germany (1965).
It is interesting to observe that the paradigm of forward recursion for n [is less than or equal to] |x| and backward recursion for n [is greater than] |x| is valid, though for different reasons, also when x is negative and Tricomi's definition of the incomplete gamma function
is used (cf.
o] are determined by the method of Molina (1915),(6) which recognizes the isomorphic relationship between the Poisson distribution function and the incomplete gamma function
In Equation (2), [Gamma] (a) is the gamma function, the integral is the incomplete gamma function
denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].