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Some formulas for the Appell function F 1 ( a, b, b ′; c; w, z )

✍ Scribed by Brychkov, Yu. A.; Saad, Nasser

Book ID
121720955
Publisher
Taylor and Francis Group
Year
2011
Tongue
English
Weight
122 KB
Volume
23
Category
Article
ISSN
1065-2469

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A finite sum representation of the Appel
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✍ A. Cuyt; K. Driver; J. Tan; B. Verdonk 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 82 KB

We use Picard's integral representation of the Appell series F1(a; b; b ; c; x; y) for Re(a) ¿ 0; Re(c -a) ¿ 0 to obtain a ÿnite sum algebraic representation of F1 in the case when a; b; b and c are positive integers with c ¿ a. The series converges for |x| ¡ 1; |y| ¡ 1 and we show that F1(a; b; b ;