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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We analyze the polynomial solutions of the linear differential equation where is a -degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials . Special cases are related to known differential equations of mathematical physics. Class... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Analytic evaluation of Gordon's integral
Jj(±p)c(b,b′;λ,w,z)=∫∞0xc+j−1e−λx1F1(b;c;wx)1F1(b′;c±p;zx)dx,
are given along with convergence conditions. It shows enormous number of definite integrals, frequently appear in theoretical and mathematical physics applications, easily ded... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The d-dimensional Schrödinger's equation is analyzed with regard to the existence of exact solutions for polynomial potentials. Under certain conditions on the interaction parameters, we show that the polynomial potentials V8(r) = ∑k = 18αkrk,α8>0 and V10(r) = ∑k = 110αkrk,α10>0 are exactly... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Using the orthonormality of the 2D-Zernike polynomials reproducing kernels, reproducing kernel Hilbert spaces and ensuing coherent states are attained. With the aid of the so obtained coherent states the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized ... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We analyze the polynomial solutions of the linear differential equation p2(x)y″+p1(x)y′+p0(x)y=0 where pj(x) is a jth-degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials pj(x). Special cases are related to known differenti... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using ... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Shannon entropy for the position and momentum eigenstates
of an asymmetric trigonometric Rosen–Morse potential
for the ground and first excited states is evaluated. The
position and momentum information entropies Sx and Sp
are calculated numerically. Also, we find that S1
x is obtained
analyticall... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The one-dimensional Schr ̈odinger’s equation is analysed w
ith regard to the existence of
exact solutions for decatic polynomial potentials. Under c
ertain conditions on the potential’s pa-
rameters, we show that the decatic polynomial potential
V
(
x
) =
ax
10
+
bx
8
+
cx
6
+
dx
4
+
ex
2
,
a >... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] Some new relations for the Appell function F 1 (a, b, b′; c; w, z) are obtained including differentiation and integration formulas, integral representations, series and recurrence relations. Some integrals are given which can be expressed in terms of F 1 and confluent Appell functions (Humbert fun... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] A simple analytic formula is derived for use in solving the Hubbell radiation rectangular source integrals . Tables of results are given to compare the numerical values derived from the approximation formula with those given earlier in the literature. |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] In this work, we study the modified beta function View the MathML source that appeared in Marus˘ić and Bajzer’s solution [M. Marus˘ić, Z˘. Bajzer, Generalized two-parameter equation of growth, J. Math. Anal. Appl. 179 (1993) 446–462] of the generalized two-parameter equation of tumor growth... |

[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] We study the generalized quantum isotonic oscillator Hamiltonian given by
𝐻
=
−
𝑑
2
/
𝑑
𝑟
2
+
𝑙
(
𝑙
+
... |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] A simple formula for computing the generalized Hubbell radiation rectangular source integralis introduced. Tables are given to compare the numerical values derived from our approximation formula with those given earlier in the literature. |

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[Page generation failure. The bibliography processor requires a browser with Javascript enabled.] The generalized hypergeometric function $_qF_p$ is a power series in which the ratio of successive terms is a rational function of the summation index. The Gaussian hypergeometric functions $_2F_1$ and $_3F_2$ are most common special cases of the generalized hypergeometric function $_qF_p$. The Appe... |