▁inline ▁speed ▁sk ating ▁International ▁Sk ating ▁Union ▁▁▁ ▁Category : W inter ▁Olympic ▁sports ▁Category : Ind ividual ▁sports ▁Category : S ports ▁origin ating ▁in ▁the ▁Netherlands ▁Category : S ports ▁origin ating ▁in ▁Norway ▁Category : D utch ▁invent ions ▁Category : I ce ▁sk ating ▁Category : Art icles ▁containing ▁video ▁cli ps <0x0A> </s> ▁In ▁mathematics , ▁the ▁family ▁of ▁Deb ye ▁functions ▁is ▁defined ▁by ▁ ▁The ▁functions ▁are ▁named ▁in ▁honor ▁of ▁Peter ▁Deb ye , ▁who ▁came ▁across ▁this ▁function ▁( with ▁n ▁= ▁ 3 ) ▁in ▁ 1 9 1 2 ▁when ▁he ▁analyt ically ▁computed ▁the ▁heat ▁capacity ▁of ▁what ▁is ▁now ▁called ▁the ▁Deb ye ▁model . ▁ ▁Mathemat ical ▁properties ▁ ▁Rel ation ▁to ▁other ▁functions ▁▁ ▁The ▁Deb ye ▁functions ▁are ▁closely ▁related ▁to ▁the ▁poly log arith m . ▁ ▁Series ▁Exp ansion ▁ ▁They ▁have ▁the ▁series ▁expansion ▁ ▁where ▁ ▁is ▁the ▁n - th ▁Bern oul li ▁number . ▁ ▁Lim iting ▁values ▁▁ ▁If ▁ ▁is ▁the ▁g amma ▁function ▁and ▁ ▁is ▁the ▁Riemann ▁z eta ▁function , ▁then , ▁for ▁, ▁ ▁Der iv ative ▁▁ ▁The ▁derivative ▁ob e ys ▁the ▁relation ▁ ▁where ▁ ▁is ▁the ▁Bern oul li ▁function . ▁ ▁App lications ▁in ▁solid - state ▁physics ▁ ▁The ▁Deb ye ▁model ▁▁ ▁The ▁Deb ye ▁model ▁has ▁a ▁density ▁of ▁v ibr ational ▁states ▁ ▁for ▁ ▁with ▁the ▁Deb ye ▁frequency ▁ ω D . ▁