# The Zagier modification of Bernoulli numbers and a polynomial extension. Part I

@article{Dixit2012TheZM, title={The Zagier modification of Bernoulli numbers and a polynomial extension. Part I}, author={Atul Abhay Dixit and Victor H. Moll and C. Vignat}, journal={The Ramanujan Journal}, year={2012}, volume={33}, pages={379-422} }

- Published 2012
DOI:10.1007/s11139-013-9484-0

AbstractThe modified Bernoulli numbers
$$ B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 $$ introduced by D. Zagier in 1998 are extended to the polynomial case by replacing Br by the Bernoulli polynomials Br(x). Properties of these new polynomials are established using the umbral method as well as classical techniques. The values of x that yield periodic subsequences $B_{2n+1}^{*}(x)$ are classified. The strange 6-periodicity of $B_{2n+1}^{*}$, established by Zagier… CONTINUE READING

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VIEW 3 EXCERPTS

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VIEW 1 EXCERPT

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 21 REFERENCES

## A modified Bernoulli number.

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## The Zagier modification of Bernoulli numbers and a polynomial extension

VIEW 2 EXCERPTS

## Bernoulli Operator and Riemann's Zeta Function

VIEW 1 EXCERPT

## The NIST Handbook of Mathematical Functions

VIEW 1 EXCERPT

## Iterated sequences and the geometry of zeros

VIEW 1 EXCERPT

## Applications of the classical umbral calculus

VIEW 2 EXCERPTS