# PROBLEMS AND RESULTS ON T ' HE CONVERGENCE AND DIVERGENCE PROPERTIES OF THE LAGRANGE INTERPOLATION POLYNOMIALS AND SOME EXTREMAL PROBLEMS

@inproceedings{ErdsPROBLEMSAR, title={PROBLEMS AND RESULTS ON T ' HE CONVERGENCE AND DIVERGENCE PROPERTIES OF THE LAGRANGE INTERPOLATION POLYNOMIALS AND SOME EXTREMAL PROBLEMS}, author={Paul Erd{\"o}s} }

Budapest In this note I will mainly discuss the joint work of Turán and mvself and some of my own results and I do not claim to give a survey of the whole subject. Let-1 c xl <. .. < xn < 1 be n points in (-1, +1). Denote bv_ l k (x) the fundamental functions of Lagrange interpolation, we have n 1, (x) = 0(x)-w(x) = L((x-xk). ~~'(xk)(x-xk~ k=1 n It is well known that the sum 1lk (x) I plays a fundamental role k=1 in the studv of the convergence and divergence properties of the Lagrauge… CONTINUE READING

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CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 19 REFERENCES

## This work ~ as communicated at the Colloquium on the Theory of Approximation of Functions

## Problems and on the theory of interpolation, (I) and (IT)

## Some remarks on Polynomials

## -16' On the theory of interpolation

## 4 property of the zeros of Legendre polynomials

## F8] On Some convergence Properties of the interpolation Polynomials

## On interpolation (I), Quadrature and mean convergence in the Lagrange interpolation

VIEW 1 EXCERPT