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For      f : [ 0 , ∞  ) →  R f:[0,\infty ) \to R       the      I M N {I_{MN}}       approximant of      f ( t ) f(t)       is  \[    I M N ( f , t ) = ∫  0 ∞  f ( x t ) ∑  i = 1 N K i e −  α  i x d x , {I_{MN}}(f,t) = \int _0^\infty {f(xt)\sum \limits _{i = 1}^N {{K_i}{e^{ - {\alpha _i}x}}dx,} }     \]  where      α  i {\alpha _i}      ,      K i {K_i}       are defined constants. Under appropriate conditions on  f ,      I M N {I_{MN}}       approximants of full grade are capable of giving good approximation both for small and large  t . These and other properties of full grade      I M N {I_{MN}}       approximants make them particularly useful in a wide range of practical applications. The constants      α  i {\alpha _i}      ,      K i {K_i}       of full grade      I M N {I_{MN}}       approximants are generated by partial fraction decompositions of certain Padé approximants to      e −  z {e^{ - z}}      . The purpose of this paper is firstly to tabulate the constants      α  i {\alpha _i}      ,      K i {K_i}       for all full grade      I M N {I_{MN}}       approximants for      1 ⩽  N ⩽  10 1 \leqslant N \leqslant 10      ; secondly, to give accurate estimates of their precision; and thirdly, to describe the methods of tabulation and estimation in sufficient detail to allow the results of this paper to be extended readily.

Tabulation of constants for full grade 𝐼_{𝑀𝑁} approximants