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In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Some authors use term discrete multiplicative integration. Thus More explicitly, if , then If F(x) is a solution of this functional equation for a given f(x), then so is CF(x) for any constant C. Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant.

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  • Indefinite product (en)
  • 乗法的不定和分 (ja)
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  • In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Some authors use term discrete multiplicative integration. Thus More explicitly, if , then If F(x) is a solution of this functional equation for a given f(x), then so is CF(x) for any constant C. Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant. (en)
  • 数学における乗法的不定和分(じょうほうてきふていわぶん、英: indefinite product; 不定乗積)∏x は、不定積分の離散版である不定和分の乗法版で、乗法的差分 Q; の逆演算である。これはまた乗法的積分の離散版であり、離散乗法的積分 (discrete multiplicative integration) と呼ぶものもある。 文献によっては、これと無関係ではないがやや異なる用法として、例えば のような形の、上の限界となる数値を特に固定せずに考えたに対して "indefinite product" の語を用いていることもあるので注意。 (ja)
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  • In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Some authors use term discrete multiplicative integration. Thus More explicitly, if , then If F(x) is a solution of this functional equation for a given f(x), then so is CF(x) for any constant C. Therefore, each indefinite product actually represents a family of functions, differing by a multiplicative constant. (en)
  • 数学における乗法的不定和分(じょうほうてきふていわぶん、英: indefinite product; 不定乗積)∏x は、不定積分の離散版である不定和分の乗法版で、乗法的差分 Q; の逆演算である。これはまた乗法的積分の離散版であり、離散乗法的積分 (discrete multiplicative integration) と呼ぶものもある。 文献によっては、これと無関係ではないがやや異なる用法として、例えば のような形の、上の限界となる数値を特に固定せずに考えたに対して "indefinite product" の語を用いていることもあるので注意。 (ja)
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