The Special Functions and Their Approximations
Yudell L. Luke
Academic Press, 1969 - Mathematics - 348 pages
A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Chapter III Hypergeometric Functions
Chapter IV Confluent Hypergeometric Functions
Chapter V The Generalized Hypergeometric Function and the GFunction
Chapter VI Identification of the pFq and GFunctions with the Special Functions of Mathematical Physics
Chapter VII Asymptotic Expansions of pFq for Large Parameters
Other editions - View all
Abramowitz and Stegun analytic continuation applications arbitrary integer arg(l argz asymptotic expansion Bernoulli polynomials Bessel functions change of notation Chapter Chebyshev polynomials coefﬁcients coeﬂicients contour convenient converges deduced deﬁned deﬁnition denominator parameter derived differential equation Erdélyi evaluation expansions in series exponential ﬁnd ﬁnite ﬁrst kind ﬁxed fundamental solutions further G-function given hypergeometric functions hypergeometric series incomplete gamma functions independent solutions inﬁnity integer or zero integrand Jacobi polynomial latter logarithmic solutions Multiply both sides negative integer Note numbers numerator parameter omit orthogonal polynomials path of integration poles proof proved Q m Q radius rational approximations recursion formula relations replaced respectively restriction right-hand side s a positive integer satisﬁes series of Chebyshev special functions suﬂicient suppose Theorem unity valid values Watson write