Plea for Diagonals and Telescopers of Rational Functions by Saoud Hassani, Jean-Marie Maillard, Nadjah Zenine

“…We introduce some challenging examples of the generalization of diagonals of rational functions, like diagonals of transcendental functions, yielding simple <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>F</mi><mn>1</mn><mn>2</mn></mmultiscripts></mrow></semantics></math></inline-formula> hypergeometric functions associated with elliptic curves, or the (differentially algebraic) lambda-extension of correlation of the Ising model.…”
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Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics by Lizana, L., Ambjornsson, T.

“…Using a Bethe ansatz we obtain the N-particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T, we arrive at an exact expression for ρT(yT,t∣yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a nonstandard asymptotic technique. …”
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The Riemann method for equations with a dominant partial derivative (A Review) by Aleksey N. Mironov, Lubov Mironova, Julia O. Yakovleva

“…In this regard, some cases are indicated when the Riemann matrix is constructed explicitly (in terms of hypergeometric functions) for such matrix equations. The paper provides a review of the literature, briefly describes the history of the development of this direction in Russia and in foreign countries.…”
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Bohr’s Phenomenon for the Solution of Second-Order Differential Equations by Saiful R. Mondal

“…The examples include several special functions like Airy functions, classical and generalized Bessel functions, error functions, confluent hypergeometric functions and associate Laguerre polynomials.…”
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Separable Boundary-Value Problems in Physics / by Willatzen, Morten, author 522551, Lew Yan Voon, Lok C., author 522552

Asymptotics, exact results, and analogies in p-adic random matrix theory by Van Peski, Roger

“…Specifically, we prove the following: (1) We show exact relations between products and corners of random matrices over Qₚ and Hall-Littlewood processes, which are direct analogues of the classical relations between singular values of real or complex random matrices and type A Heckman-Opdam hypergeometric functions. (2) We prove that the boundary of the Hall-Littlewood t-deformation of the Gelfand-Tsetlin graph is parametrized by infinite integer signatures, extending results of Gorin and Cuenca on boundaries of related deformed Gelfand-Tsetlin graphs. (3) In the special case when 1/t is a prime p we combine this with the aforementioned relations between matrix corners and Hall-Littlewood polynomials to recover results of Bufetov-Qiu [BQ17] and Assiotis [Ass20] on infinite p-adic random matrices. (4) Using the above relation between matrix products and Hall-Littlewood polynomials, together with explicit formulas for the latter, we obtain exact product formulas for the joint distribution of the cokernels of products A₁,A₂A₁,A₃A₂A₁, . . . of independent additive-Haar-distributed matrices A subscript i over the p-adic integers Zₚ. …”
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Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey by Virginia Kiryakova, Jordanka Paneva-Konovska

“…In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox <i>H</i>-functions, the Fox–Wright generalized hypergeometric functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow></mrow><mi>p</mi></msub><msub><mo>Ψ</mo><mi>q</mi></msub></mrow></semantics></math></inline-formula> and a large number of their representatives. …”
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Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids by Viktor V. Dodonov, Matheus B. Horovits

“…Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. …”
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Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with... by Sanae Rujivan, Athinan Sutchada, Kittisak Chumpong, Napat Rujeerapaiboon

“…We analytically solve this problem by showing that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>γ</mi><mi>th</mi></msup></semantics></math></inline-formula> moment of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mi>n</mi></msub></semantics></math></inline-formula> can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>γ</mi><mi>th</mi></msup></semantics></math></inline-formula> moment of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mi>n</mi></msub></semantics></math></inline-formula> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>X</mi><mi>i</mi></msub></semantics></math></inline-formula> is a combination of statistically independent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>Z</mi><mi>i</mi><mn>2</mn></msubsup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>i</mi></msub></semantics></math></inline-formula> in which the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mi>i</mi></msub></semantics></math></inline-formula>’s are distributed according to normal or Maxwell–Boltzmann distributions and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>i</mi></msub></semantics></math></inline-formula>’s are distributed according to gamma, Erlang, or exponential distributions. …”
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Novel Outlook on the Eigenvalue Problem for the Orbital Angular Momentum Operator by George Japaridze, Anzor Khelashvili, Koba Turashvili

“…The normalizable eigenfunctions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover accent="true"><mi>M</mi><mo stretchy="false">^</mo></mover><mn>2</mn></msup></semantics></math></inline-formula> are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. …”
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