# Analytic Representation of Maxwell—Boltzmann and Tsallis Thermonuclear Functions with Depleted Tail

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## Abstract

**:**

## 1. Introduction

#### 1.1. Non-Resonant Case with High Energy Cut-OFF

#### 1.2. Non-Resonant Case with Depleted Tail

#### 1.3. Non-Resonant Case with Screening

## 2. Standard Non-Resonant Thermonuclear Functions with Depleted Tail

## 3. Extension of the Non-Resonant Thermonuclear Function with Depleted Tail

## 4. Comparison of the Extended Results with the Standard Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) ${f}_{MBD}\left(E\right)$ for $kT=100,200,300$. (

**b**) ${f}_{PD}\left(E\right)$ for $kT=100,\alpha =1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.2,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.3,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.5$ and $\alpha =1.6$. (

**c**) ${f}_{PD}\left(E\right)$ for $kT=200,\alpha =1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.2,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.3,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.5$ and $\alpha =1.6$. (

**d**) ${f}_{PD}\left(E\right)$ for $kT=300,\alpha =1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.1,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.2,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.3,\phantom{\rule{3.33333pt}{0ex}}\alpha =1.5$ and $\alpha =1.6$.

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**MDPI and ACS Style**

Kumar, D.; Haubold, H.J.
Analytic Representation of Maxwell—Boltzmann and Tsallis Thermonuclear Functions with Depleted Tail. *Axioms* **2021**, *10*, 115.
https://doi.org/10.3390/axioms10020115

**AMA Style**

Kumar D, Haubold HJ.
Analytic Representation of Maxwell—Boltzmann and Tsallis Thermonuclear Functions with Depleted Tail. *Axioms*. 2021; 10(2):115.
https://doi.org/10.3390/axioms10020115

**Chicago/Turabian Style**

Kumar, Dilip, and Hans J. Haubold.
2021. "Analytic Representation of Maxwell—Boltzmann and Tsallis Thermonuclear Functions with Depleted Tail" *Axioms* 10, no. 2: 115.
https://doi.org/10.3390/axioms10020115