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Anixx
Anixx
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I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:

$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$

It is interesting because it is claimed that roots of any polynomial can be expressed in this function and elementary functions. Is this true and how the roots of arbitrary polynomial can be expressed?

P.S. In Mathematica this function is inplemented as QPochhammer[q]

I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:

$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$

It is interesting because it is claimed that roots of any polynomial can be expressed in this function and elementary functions. Is this true and how the roots of arbitrary polynomial can be expressed?

I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:

$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$

It is interesting because it is claimed that roots of any polynomial can be expressed in this function and elementary functions. Is this true and how the roots of arbitrary polynomial can be expressed?

P.S. In Mathematica this function is inplemented as QPochhammer[q]

Source Link
Anixx
Anixx
  • 10.1k
  • 4
  • 39
  • 63

Can roots of any polynomial be expressed using Eulerian function?

I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:

$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$

It is interesting because it is claimed that roots of any polynomial can be expressed in this function and elementary functions. Is this true and how the roots of arbitrary polynomial can be expressed?