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Special Functions: An Introduction to the Classical Functions of Mathematical Physics
Bernoulli, Euler and Stirling Numbers. Useful Methods and Techniques. The Gamma Function. Differential Equations. Hypergeometric Functions. Orthogonal Polynomials. Confluent Hypergeometric Functions.Expand
Numerical methods for special functions
TLDR
This book provides an up-to-date overview of methods for computing special functions and discusses when to use them in standard parameter domains, as well as in large and complex domains. Expand
Uniform Airy-type expansions of integrals
A new method for representing the remainder and coefficients in Airy-type expansions of integrals is given. The quantities are written in terms of Cauchy-type integrals and are naturalExpand
The asymptotic expansion of the incomplete gamma functions : (preprint)
Earlier investigations on uniform asymptotic expansions of the incomplete gamma functions are reconsidered. The new results include estimations for the remainder and the extension of the results toExpand
Asymptotic and numerical aspects of the noncentral chi-square distribution
Abstract The concentral χ2-distribution is related with the series e −x ∑ n=0 ∞ x n n! P(μ+ n, y)=1− e −x ∑ n=0 ∞ ∞ n n! Q(μ+n, y) where P(α, z) and Q(α, z) are incomplete gamma functions (centralExpand
Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function : (prepublication)
New asymptotic expansions are derived for the incomplete gamma functions and the incomplete beta function. In each case the expansion contains the complementary error function and an asymptoticExpand
Critical conditions for phytoplankton blooms
TLDR
The results show that the conditions for phytoplankton bloom development can be captured by a critical depth, a compensation depth, and zero, one or two critical values of the vertical turbulent diffusion coefficient. Expand
The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions
An asymptotic expansion is given for a class of integrals for large values of a parameter, which corresponds with the degrees of freedom in a certain type of cumulative distribution functions. TheExpand
ASYMPTOTIC ESTIMATES FOR GENERALIZED STIRLING NUMBERS
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. TheExpand
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