Higher Transcendental Functions, Volume 2McGraw-Hill, 1953 - Transcendental functions |
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Page 326
... poles in a cell , each pole counted according to its multiplicity , is called the order of the elliptic function . The set of poles or zeros in a given cell is called an irreducible set . The sum of the residues of an elliptic function ...
... poles in a cell , each pole counted according to its multiplicity , is called the order of the elliptic function . The set of poles or zeros in a given cell is called an irreducible set . The sum of the residues of an elliptic function ...
Page 336
... poles at all , 0309 is an elliptic function since irreducible set of poles , is zero an elliptic function for s = 2 , 3 , tion . Since the principal part of follows that ( z ) has no poles at and thus is constant . Any elliptic function ...
... poles at all , 0309 is an elliptic function since irreducible set of poles , is zero an elliptic function for s = 2 , 3 , tion . Since the principal part of follows that ( z ) has no poles at and thus is constant . Any elliptic function ...
Page 337
... poles of ƒ ( z ) , each repeated h B ,, ... , according to its multiplicity . We know ( sec . 13.11 ) that r = 1 ( a , - , ) is a period , and replacing some of the zeros and poles by congruent ones , we may assume that ( a , - B ) = 0 ...
... poles of ƒ ( z ) , each repeated h B ,, ... , according to its multiplicity . We know ( sec . 13.11 ) that r = 1 ( a , - , ) is a period , and replacing some of the zeros and poles by congruent ones , we may assume that ( a , - B ) = 0 ...
Contents
BESSEL FUNCTIONS | 1 |
Modified Bessel functions of integer order | 9 |
4 | 22 |
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˝ π ˝µ ˝π a₁ addition theorem Akad algebraic Amer Bessel functions coefficients complex convergence corresponding cosh defined denotes derived differential equation elliptic integrals Erdélyi expressed in terms finite formulas ƒŞ Gegenbauer Gegenbauer polynomials given H₂ harmonic polynomial hence Hermite polynomials hypergeometric functions integral representations J₂ Jacobi polynomials Jacobian elliptic functions Ju+n Koschmieder Laguerre polynomials Legendre Legendre's London Math Meijer nomials notation obtain orthogonal polynomials poles polynomial of degree Proc proved rational function recurrence relation second kind sin˛ sinh surface harmonics Szegő theory theta functions third kind transformation Tricomi values variable Watson Weierstrass weight function г ˝