• Corpus ID: 63998763

Handbook Of Mathematical Functions

@inproceedings{Gerber2016HandbookOM,
  title={Handbook Of Mathematical Functions},
  author={Thorsten Gerber},
  year={2016}
}
 

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References

SHOWING 1-10 OF 15 REFERENCES
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
A handbook of mathematical functions that is designed to provide scientific investigations with a comprehensive and self-contained summary of the mathematical functions that arise in physical and
Solving equations exactly
The problem of the solution of a given se t of lin ear equations Ax = b on a high-speed digital computer has been studied intensively, and there are a large number of method s, more or less sati
Numerical solution of second-order linear difference equations
A ne w al~orilhm is ~ive n fur cumpulin ~ Ihe soluliun of a ny secu nd-orde r lin ea r diffe re nce e qua lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau se uf
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.
Lowan , The Computation Laboratory of the National Bureau of Standards , Scripta Math
    Digital Library of Mathematical Functions, (http://dlmf.nist.gov) National Institute of Standards and Technology
    • Digital Library of Mathematical Functions, (http://dlmf.nist.gov) National Institute of Standards and Technology
    Integral Matrices
    • 1972
    Y1(x), K0(x), K1(x) 0< = x< = 1
    • Y1(x), K0(x), K1(x) 0< = x< = 1
    • 1948
    ...
    ...