Special Functions Of Mathematical Physics: A Unified Introduction With Applications
by NIKIFOROV /
2013 / English / PDF
25 MB Download
With students of Physics chiefly in mind, we have collected the
material on special functions that is most important in
mathematical physics and quan tum mechanics. We have not attempted
to provide the most extensive collec tion possible of information
about special functions, but have set ourselves the task of finding
an exposition which, based on a unified approach, ensures the
possibility of applying the theory in other natural sciences, since
it pro vides a simple and effective method for the independent
solution of problems that arise in practice in physics, engineering
and mathematics. For the American edition we have been able to
improve a number of proofs; in particular, we have given a new
proof of the basic theorem (§3). This is the fundamental theorem of
the book; it has now been extended to cover difference equations of
hypergeometric type (§§12, 13). Several sections have been
simplified and contain new material. We believe that this is the
first time that the theory of classical or thogonal polynomials of
a discrete variable on both uniform and nonuniform lattices has
been given such a coherent presentation, together with its various
applications in physics.
With students of Physics chiefly in mind, we have collected the
material on special functions that is most important in
mathematical physics and quan tum mechanics. We have not attempted
to provide the most extensive collec tion possible of information
about special functions, but have set ourselves the task of finding
an exposition which, based on a unified approach, ensures the
possibility of applying the theory in other natural sciences, since
it pro vides a simple and effective method for the independent
solution of problems that arise in practice in physics, engineering
and mathematics. For the American edition we have been able to
improve a number of proofs; in particular, we have given a new
proof of the basic theorem (§3). This is the fundamental theorem of
the book; it has now been extended to cover difference equations of
hypergeometric type (§§12, 13). Several sections have been
simplified and contain new material. We believe that this is the
first time that the theory of classical or thogonal polynomials of
a discrete variable on both uniform and nonuniform lattices has
been given such a coherent presentation, together with its various
applications in physics.