劉俊評 asked in 科學數學 · 1 decade ago

Gamma函數

大家好~~~~

我想請問 Γ(0) Γ(-1) Γ(-2)

這些是多少? 能解釋一下嗎??

請各位大大回答~~~~感恩

Update:

請問能再講解的白話文一點嗎????

謝謝

1 Answer

Rating
  • 天助
    Lv 7
    1 decade ago
    Favorite Answer

    Definition: Γ(a)=∫[0~∞] t^(a-1) exp(-t) dt, for a>0.

    (1)Γ(0) is defined as ∫[0~∞] exp(-t)/t dt formly.

    while ∫[0~∞] exp(-t)/t dt

    >∫[0~1] exp(-1)/t dt= (1/e) lim(t->0+) ln|t|=∞

    so Γ(0)=∞

    (2)Γ(a) (a<0) is defined as ∫[0~∞] exp(-t)/t^(1-a) dt formly.

    while ∫[0~∞] exp(-t)/t^(1-a) dt

    >∫[0~1] exp(-1)/t^(1-a) dt= [1/(ae)] lim(t->0+) (1-t^a)=∞

    so Γ(-1)=∞, Γ(-2)=∞

    2010-06-01 02:32:29 補充:

    Γ(a)=∫[0~∞] t^(a-1) exp(-t) dt

    a > 0,則瑕積分收斂

    a <= 0,則瑕積分在t -> 0+處發散

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