TY - JOUR
T1 - On an extension of Kummer's second theorem
AU - Rakha, Medhat A.
AU - Awad, Mohamed M.
AU - Rathie, Arjun K.
PY - 2013
Y1 - 2013
N2 - The aim of this paper is to establish an extension of Kummer's second theorem in the form e - x / 2 F 2 2 [ a, 2 + d; x 2 a + 2, d; ] = F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + ((a / d - 1 / 2) / (a + 1)) x F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + (c x 2 / 2 (2 a + 3)) F 1 0 [ -; x 2 / 16 a + 5 / 2; ], where c = 1 / a + 1 1 / 2 - a / d + a / d (d + 1), d ≠ 0, - 1, - 2,. For d = 2 a, we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminating F 2 3 (2) series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.
AB - The aim of this paper is to establish an extension of Kummer's second theorem in the form e - x / 2 F 2 2 [ a, 2 + d; x 2 a + 2, d; ] = F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + ((a / d - 1 / 2) / (a + 1)) x F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + (c x 2 / 2 (2 a + 3)) F 1 0 [ -; x 2 / 16 a + 5 / 2; ], where c = 1 / a + 1 1 / 2 - a / d + a / d (d + 1), d ≠ 0, - 1, - 2,. For d = 2 a, we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminating F 2 3 (2) series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.
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U2 - 10.1155/2013/128458
DO - 10.1155/2013/128458
M3 - Article
AN - SCOPUS:84877291371
SN - 1085-3375
VL - 2013
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
M1 - 128458
ER -