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The luminosity distance in the standard cosmology as given by $\Lambda$CDMand consequently the distance modulus for supernovae can be defined by thePad\'e approximant. A comparison with a known analytical solution shows thatthe Pad\'e approximant for the luminosity distance has an error of $4\%$ atredshift $= 10$. A similar procedure for the Taylor expansion of the luminositydistance gives an error of $4\%$ at redshift $=0.7 $; this means that for theluminosity distance, the Pad\'e approximation is superior to the Taylor series.The availability of an analytical expression for the distance modulus allowsapplying the Levenberg--Marquardt method to derive the fundamental parametersfrom the available compilations for supernovae. A new luminosity function forgalaxies derived from the truncated gamma probability density function modelsthe observed luminosity function for galaxies when the observed range inabsolute magnitude is modeled by the Pad\'e approximant. A comparison of$\Lambda$CDM with other cosmologies is done adopting a statistical point ofview.

Pad\'e Approximant and Minimax Rational Approximation in Standard Cosmology