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We present examples of Pad&#233; approximations of the <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold rotation-symmetric flow where eddy viscosity is negative, indicating intervals of large-scale instability of the flow. Turning to the kinematic dynamo problem for three-dimensional flows of an incompressible fluid, we explore the application of Pad&#233; approximants for the computation of tensors of magnetic <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-effect and, for parity-invariant flows, of magnetic eddy diffusivity. We construct Pad&#233; approximants of the tensors expanded in power series in the inverse molecular diffusivity <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>/</mo> <mi>&#951;</mi> </mrow> </semantics> </math> </inline-formula> around <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>/</mo> <mi>&#951;</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>. This yields the values of the dominant growth rate to satisfactory accuracy for <inline-formula> <math display="inline"> <semantics> <mi>&#951;</mi> </semantics> </math> </inline-formula>, several dozen times smaller than the threshold, above which the power series is convergent. We do computations in Fortran in the standard &#8220;double&#8221; (real*8) and extended &#8220;quadruple&#8221; (real*16) precision, and perform symbolic calculations in Mathematica.