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trigam
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There are 6 letters in TRIGAM ( A1G2I1M3R1T1 )
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Definitions of trigam in various dictionaries:
TRIGAM - In mathematics, the trigamma function, denoted ψ1(z), is the second of the polygamma functions, and is defined by ...
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In mathematics, the trigamma function, denoted ψ1(z), is the second of the polygamma functions, and is defined by* * * * * ψ * * 1 * * * ( * z * ) * = * * * * d * * 2 * * * * d * * z * * 2 * * * * * * ln * * Γ * ( * z * ) * * * {\displaystyle \psi _{1}(z)={\frac {d^{2}}{dz^{2}}}\ln \Gamma (z)} * .It follows from this definition that * * * * * * ψ * * 1 * * * ( * z * ) * = * * * d * * d * z * * * * ψ * ( * z * ) * * * {\displaystyle \psi _{1}(z)={\frac {d}{dz}}\psi (z)} * where ψ(z) is the digamma function. It may also be defined as the sum of the series * * * * * * ψ * * 1 * * * ( * z * ) * = * * ∑ * * n * = * 0 * * * ∞ * * * * * 1 * * ( * z * + * n * * ) * * 2 * * * * * * , * * * {\displaystyle \psi _{1}(z)=\sum _{n=0}^{\infty }{\frac {1}{(z+n)^{2}}},} * making it a special case of the Hurwitz zeta function * * * * * * ψ * * 1 * * * ( * z * ) * = * ζ * ( * 2 * , * z * ) * . * * * {\displaystyle \psi _{1}(z)=\zeta (2,z).} * Note that the last two formulas are valid when 1 − z is not a natural number. |