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Asymptotics and Special Functions
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
NIST Handbook of Mathematical Functions
TLDR
This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.
The asymptotic expansion of bessel functions of large order
  • F. Olver
  • Mathematics
    Philosophical Transactions of the Royal Society…
  • 28 December 1954
New expansions are obtained for the functions Iv{yz), ) and their derivatives in terms of elementary functions, and for the functions J v(vz), Yv{vz), H fvz) and their derivatives in terms of Airy
Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral
By allowing the number of terms in an asymptotic expansion to depend on the asymptotic variable, it is possible to obtain an error term that is exponentially small as the asymptotic variable tends to
Second-order linear differential equations with two turning points
  • F. Olver
  • Mathematics
    Philosophical Transactions of the Royal Society…
  • 20 March 1975
Differential equations of the form d2w/dx2={u2f(u,a,x)+g(u,a,x)}w are considered for large values of the real parameter u. Here x is a real variable ranging over an open, possibly infinite, interval
Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders
a re sought for la rge values of IILI, which a re uniformly valid wi th respect Lo a rg IL and un restricted va lues of the complex variable t. Two types of expa nsion are found . Those of the first
Error Bounds for Stationary Phase Approximations
An error theory is constructed for the method of stationary phase for integrals of the \[I(x) = \int_a^b {e^{ixp(t)} q(t)dt.} \]Here x is a large real parameter, the function $p(t)$ is real, and
Digital Library of Mathematical Functions
TLDR
This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
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