scholarly journals Higher-order QCD corrections to hadronic τ decays from Padé approximants

2018 ◽  
Vol 2018 (8) ◽  
Author(s):  
Diogo Boito ◽  
Pere Masjuan ◽  
Fabio Oliani
Keyword(s):  
Padé Approximants ◽  
Higher Order ◽  
Pade Approximants

Partial differential approximants for multivariable power series. II. Invariance properties

1983 ◽  
Vol 388 (1794) ◽  
pp. 75-102 ◽  
Keyword(s):  
Power Series ◽  
Padé Approximants ◽  
Higher Order ◽  
Rotational Invariance ◽  
Linear Transformations ◽  
Partial Differential ◽  
Original Series ◽  
Pade Approximants ◽  
Invariance Properties ◽  
Change Of Variables

The invariance properties of partial differential approximants for power series in two (or more) variables are investigated. Certain classes of approximants are shown to exhibit desirable properties such as : ( a ) Eulerian invariance under the change of variables x => ̅x = Ax /(1+ Bx ) and/or y => ̅y = Cy / (1+ Dy ); ( b ) ‘rotational’ invariance under homo­geneous linear transformations of x and y ; ( c ) covariance under exponentiation of the original series. Similar results are demonstrated for constrained, multipoint, and higher order differential approximants. Specializing to functions of one variable provides extensions of known invariance properties of ordinary Padé approximants and inhomogeneous differential approximants.

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