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Euler-Riemann's zeta and Dirichlet's eta functions are defined for real negative numbers as analytic continuation. In the present book the author defines new series for zeta and eta functions, for real negative and imaginary numbers without analytic continuation. The new zeta and eta functions maintain the character of harmonic series and alternating harmonic series respectively for real negative numbers, as for real positive numbers. Zeta and eta functions have also been defined for multiple- and fractional harmonic series.

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9781518608636

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Dr. A.K.Thukral, Professor at Guru Nanak Dev University, got his Ph.D. (1980) from BITS, Pilani, India. He was a Postdoctoral fellow (1984-86) at the Moscow State University, Moscow. He has been on the faculty of Guru Nanak Dev University since 1980. Dr. Thukral specialises in Environmental Sciences. He has supervised 15 Ph.D. students, published more than 125 research papers, edited 2 books and attended several conferences. He has held various academic positions, such as Head of the Department, Dean of the Faculty, Dean of Student's Welfare and Director of Research. He is a crusader of integrated and interdisciplinary education and research.

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