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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 functions) Φ1, Φ2, Φ3.
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Brychkov et al. (2011) studied this question.
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