Series2

Description

Series2 performs a series expansion around 0. Series2 is (up to the Gamma - bug) equivalent to Series, except that it applies Normal on the result and has an option FinalSubstitutions. Series2[f, e, n] is equivalent to Series2[f, {e, 0, n}].

Options[Series2]

Examples

Series2[(x (1 - x))^(δ/2), δ, 1]

Series2[Gamma[x], x, 1]

Series[Gamma[x], {x, 0, 1}]

Series2[Gamma[x], x, 2]

Series2[Gamma[x], x, 2, FinalSubstitutions -> {}] // 
      FullSimplify

Series[Gamma[x], {x, 0, 4}] // Normal // FullSimplify

There is a table of expansions of special hypergeometric functions.

Series2[
      HypergeometricPFQ[{1, OPEm - 1, Epsilon/2 + OPEm}, {OPEm, 
          OPEm + Epsilon}, 1], {Epsilon, 0, 1}]

Series2[
      HypergeometricPFQ[{1,  OPEm,  
          Epsilon/2  +  OPEm},  {1  +  OPEm,  Epsilon  +  OPEm},   
        1], {Epsilon, 0, 1}]

Hypergeometric2F1[1,  Epsilon,  1  +  2 Epsilon, x]

Series2[%, {Epsilon, 0, 3}]

There are over 100 more special expansions of (Subscript[ , 2])(Subscript[F, 1]) tabulated in Series2.m. The interested user can consult the source code (search for HYPERLIST).