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This volume provides a systematic survey of almost all the
equivalent assertions to the functional equations - zeta symmetry -
which zeta-functions satisfy, thus streamlining previously
published results on zeta-functions. The equivalent relations are
given in the form of modular relations in Fox H-function series,
which at present include all that have been considered as
candidates for ingredients of a series. The results are presented
in a clear and simple manner for readers to readily apply without
much knowledge of zeta-functions.This volume aims to keep a record
of the 150-year-old heritage starting from Riemann on
zeta-functions, which are ubiquitous in all mathematical sciences,
wherever there is a notion of the norm. It provides almost all
possible equivalent relations to the zeta-functions without
requiring a reader's deep knowledge on their definitions. This can
be an ideal reference book for those studying zeta-functions.
This book (Vista II), is a sequel to Vistas of Special Functions
(World Scientific, 2007), in which the authors made a unification
of several formulas scattered around the relevant literature under
the guiding principle of viewing them as manifestations of the
functional equations of associated zeta-functions. In Vista II,
which maintains the spirit of the theory of special functions
through zeta-functions, the authors base their theory on a theorem
which gives some arithmetical Fourier series as intermediate
modular relations - avatars of the functional equations. Vista II
gives an organic and elucidating presentation of the situations
where special functions can be effectively used. Vista II will
provide the reader ample opportunity to find suitable formulas and
the means to apply them to practical problems for actual research.
It can even be used during tutorials for paper writing.
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Paperback
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R398
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Discovery Miles 3 300
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