Uniform approximation by polynomials on an interval of Bessel functions with an integral index

1975 ◽  
Vol 26 (5) ◽  
pp. 561-564
Author(s):  
V. K. Stolyarchuk
Keyword(s):  
Uniform Approximation ◽  
Bessel Functions ◽  
Integral Index ◽  
Approximation By Polynomials

scholarly journals A note on uniform approximation of functions having a double pole

2014 ◽  
Vol 17 (1) ◽  
pp. 233-244
Author(s):  
Ionela Moale ◽  
Veronika Pillwein
Keyword(s):  
Symbolic Computation ◽  
Uniform Approximation ◽  
Classical Problem ◽  
Type Equation ◽  
Elliptic Functions ◽  
Double Pole ◽  
Approximation Of Functions ◽  
Best Uniform Approximation ◽  
Approximation By Polynomials ◽  
Low Degrees

AbstractWe consider the classical problem of finding the best uniform approximation by polynomials of$1/(x-a)^2,$where$a>1$is given, on the interval$[-\! 1,1]$. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.

Uniform approximation by polynomials in two functions

1989 ◽  
Vol 284 (4) ◽  
pp. 529-535 ◽  
Author(s):  
A. G. O'Farrell ◽  
K. J. Preskenis
Keyword(s):  
Uniform Approximation ◽  
Approximation By Polynomials

Asymptotic expansions for the hypergeometric functions occurring in gas-flow theory

1950 ◽  
Vol 202 (1071) ◽  
pp. 507-522 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Uniform Approximation ◽  
Hypergeometric Functions ◽  
Gas Flow ◽  
Bessel Functions ◽  
Flow Theory ◽  
Gas Flows ◽  
Hodograph Method ◽  
Asymptotic Formulae ◽  
Circular Functions

Asymptotic formulae of two sorts are found for the hypergeometric functions, of large order v , which arise when gas-flows are investigated by the hodograph method. These functions are monotonic for 'subsonic’ values of the argument T , oscillating for ‘supersonic’ values. (i) Elementary formulae, involving exponential or circular functions and singular at the sonic value T = T s , are developed to the terms in v -4 . When T is near T s these formulae give poor approximation, (ii) Formulae giving uniform approximation near T S involving Bessel functions, are developed to the terms in v -4 . These give 7-figure accuracy over the physically significant range of T , for │ v │ ≥ 10. The coefficients are tabulated for T = 0 (0·02) 0·50 for the case where the adiabatic index γ of the gas is 1·4.

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