The jacobi inversion formula

The Addition Formula for Jacobi Polynomials

Recently the author derived a Laplace integral representation, a product formula and an addition formula for Jacobi polynomials Ppfi). The results are (1) (2) and (3) * j, ,I " (~0~2 0-f-2 sin2 0 + ir cos #I sin 28)n * ' P$ycos 281) PFycos 282) 2&x + 1) Pgq 1) Pfq 1)-= l/22 qa-p)r(/l+#. . .

The Lagrange Inversion Formula and Divisibility Properties

Wilf stated that the Lagrange inversion formula (LIF) is a remarkable tool for solving certain kinds of functional equations, and at its best it can give explicit formulas where other approaches run into stone walls. Here we present the LIF combinatorially in the form of lattice paths, and apply it to the divisibility property of the coefficients of a formal power series expansion. For the LIF,...

The Planar Tree Lagrange Inversion Formula

Inverse Measures , the Inversion Formula , andDiscontinuous

The present paper is part I of a series of three closely related papers in which the inverse measure (dt) of a given measure (dt) on 0; 1] is introduced. In the rst case discussed in detail, and are multifractal in the usual sense, that is, both are linearly self-similar and continuous but not diierentiable and both are non{zero for every interval of 0; 1]. Under these assumptions the HH older ...

Inversion Formula for Continuous Multifractals

In a previous paper MR the authors introduced the inverse measure y of a probability measure on It was argued that the respective multifractal spectra are linked by the inversion formula fy f Here the statements of MR are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures Thereby f may stand for the Hausdor spectrum the packing spect...