Gamma function approximationWhen h → 0, Γ ( h + α ) ⋅ h Γ ( h + 1 ) ∼ Γ ( α ) ⋅ h

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Gamma function approximationWhen   h  →  0,                     Γ        (        h        +        α        )        ⋅        h                    Γ        (        h        +        1        )              ∼  Γ  (  α  )  ⋅  h

hi3c4a2nvrgzb · Accepted Answer

lim              h        →        0                                      Γ          (          h          +          α          )                    h                          Γ          (          h          +          1          )                    Γ          (          α          )                    h                      =          lim              h        →        0                                      Γ          (          h          +          α          )                          Γ          (          h          +          1          )                    Γ          (          α          )                                              =          ⏟                            Γ         continuous                            Γ        (        α        )                    Γ        (        1        )        Γ        (        α        )              =    1.

Ainsley Zimmerman · Accepted Answer

Since   x  ↦  Γ  (  ⋅  ) is a continuous function, as   h  →  0, one has  Γ  (  h  +  α  )  ∼  Γ  (  0  +  α  )  =  Γ  (  α  )  ,    Γ  (  h  +  1  )  ∼  Γ  (  1  )  =  1giving                    Γ        (        h        +        α        )        ⋅        h                    Γ        (        h        +        1        )              ∼                    Γ        (        0        +        α        )        ⋅        h                    Γ        (        0        +        1        )              =  Γ  (  α  )  ⋅  h

Gamma function approximation When h → 0 , <mstyle displaystyle="tru

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