In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: It is the first of the polygamma functions. This function is strictly increasing and strictly concave on , and it asymptotically behaves as for large arguments ( ) in the sector with some infinitesimally small positive constant .
The name digamma was used in ancient Greek and is the most common name for the letter in its alphabetic function today. It literally means "double gamma " and is descriptive of the original letter's shape, which looked like a Γ (gamma) placed on top of another.
Later, when the sound was lost, it was called "Digamma", which means "double Gamma ", because it looks like a Gamma (Γ) with two hooks. The Latin letter F was also taken over from Wau. In mathematics, the name "digamma" is used in digamma function, which is the derivative of the logarithm of gamma function (that is, ).
From this, we can find specific values of the digamma function easily; for example, putting s=0, s = 0, we get \psi (1)=-\gamma. ψ(1) = −γ. \psi (s+1) = -\gamma + H_s. ψ(s+1) = −γ +H s.
ウェブIn mathematics, the polygamma function of order m is a meromorphic function on the complex numbers defined as the (m + 1) th derivative of the logarithm of the gamma …
ウェブThe digamma function is a special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the …