AN EXTENSION OF A KUMMER'S QUADRATIC TRANSFORMATION FORMULA WITH AN APPLICATION
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In the theory of the generalized hypergeometric functions,a remarkable amount of mathematicians's concern has been given to developtheir transformation formulas and summation identities. Here weaim at presenting a new and (potentially) useful transformation formulafor hypergeometric functions [수식] Further we apply theso-called beta integral method which was used systematically by Krattenthalerand Rao to the Kummer's quadratic transformation formulaand the above-presented transformation formula and present (presumablynew) transformation formulas for hypergeometric series. Relevantconnections of some special cases of the results presented here with thoseobtained in earlier works are also pointed out.
Abstract
In the theory of the generalized hypergeometric functions,a remarkable amount of mathematicians's concern has been given to developtheir transformation formulas and summation identities. Here weaim at presenting a new and (potentially) useful transformation formulafor hypergeometric functions [수식] Further we apply theso-called beta integral method which was used systematically by Krattenthalerand Rao to the Kummer's quadratic transformation formulaand the above-presented transformation formula and present (presumablynew) transformation formulas for hypergeometric series. Relevantconnections of some special cases of the results presented here with thoseobtained in earlier works are also pointed out.
참고문헌 (18)
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