Derivatives of Horn hypergeometric functions with respect to their parameters

Ancarani, L. U.; Punta, J. A. Del; Gasaneo, Gustavo

doi:10.1063/1.4994059

Cited by 12 publications

(11 citation statements)

References 37 publications

(57 reference statements)

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“…Appell functions can be found in the study of autoionization of atoms [10], separability of Hamilton-Jacobi equations in classical mechanics [11], representation of Feynmann integral in quantum field theory [3,4], and expression of Nordsieck integral in atomic collisions physics [12]. Another generalization of hypergeometric functions is the hypergeometric k -function, defined by the Pochhammer k-symbol studied by Diaz et al [13].…”

Section: Introductionmentioning

confidence: 99%

On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

2020

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Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol Diaz et al. 2017, which are one of the vital generalizations of hypergeometric functions. We introduce k-analogues of F2and F3 Appell functions denoted by the symbols F2,kand F3,k,respectively, just like Mubeen et al. did for F1 in 2015. Meanwhile, we prove integral representations of the k-generalizations of F2and F3 which provide us with an opportunity to generalize widely used identities for Appell hypergeometric functions. In addition, we present some important transformation formulas and some reduction formulas which show close relation not only with k-Appell functions but also with k-hypergeometric functions. Finally, employing the theory of Riemann–Liouville k-fractional derivative from Rahman et al. 2020, and using the relations which we consider in this paper, we acquire linear and bilinear generating relations for k-analogue of hypergeometric functions and Appell functions.

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Section: Introductionmentioning

confidence: 99%

On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

2020

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“…where 1 (a, b, c 1 , c 2 ; z 1 , z 2 ) is the two-variable (degenerate) confluent hypergeometric series [21,22], given by [23]:…”

Section: Evaluation Of N D ( P)mentioning

confidence: 99%

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

2021

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For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $$\rho _\mathrm{B}$$ ρ B in terms of center of mass and relative coordinates of the particles. The deviation from $$\rho _\mathrm{F}$$ ρ F , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained $$\rho _\mathrm{B}$$ ρ B allows us to derive a closed form expression of the corresponding momentum distribution $$n_\mathrm{B}(p)$$ n B ( p ) . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum $$1/p^4 $$ 1 / p 4 tail with the appropriate Tan’s coefficient. Numerical results support our findings.

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“…Let us start with the second term of the first double integral I 1 in (19), and perform an integration by parts with respect to u, to get…”

Section: B Evaluation Of Nd(p)mentioning

confidence: 99%

“…Combining now the two terms, and integrating over u (simple Gaussian-type integral [15]), the first double integral in (19) simplifies into…”

Section: B Evaluation Of Nd(p)mentioning

confidence: 99%

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The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

Bencheikh

Nieto

Ancarani

2021

Preprint

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For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix ρB in terms of centre of mass and relative coordinates of the particles. The deviation from ρF , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained ρB allows us to derive a closed form expression of the corresponding momentum distribution nB(p). We show how the result deviates from the noninteracting fermionic case, the deviation being associated to the short range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum 1/p 4 tail with the appropriate Tan's coefficient. Numerical results support our findings.

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Derivatives of Horn hypergeometric functions with respect to their parameters

Cited by 12 publications

References 37 publications

On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

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