# Results

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[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... |

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[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. |

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[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... |

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

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[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.] Infinite series of the type Sigma(n=1)(infinity)(alpha/2)n/n 1/n!F-2(1)(-n,b;gamma;y) are investigated. Closed-form sums are obtained for alpha a positive integer, alpha = 1, 2, 3,.... The limiting case of b --> infinity, after gamma is replaced with x(2)/b, leads to Sigma(n=1)(infinity)(alpha/2)... |

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