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 -