連續q-哈恩多項式以基本超幾何函數定義：[1] p n ( x ; a , b , c | q ) = a − n e − i n u ( a b e 2 i u , a c , a d ; q ) n ∗ 4 Φ 3 ( q − n , a b c d q n − 1 , a e i t + 2 u , a e − i t ; a b e 2 i u , a c , a d ; q ; q ) {\displaystyle p_{n}(x;a,b,c|q)=a^{-n}e^{-inu}(abe^{2iu},ac,ad;q)_{n}*_{4}\Phi _{3}(q^{-n},abcdq^{n-1},ae^{i{t+2u}},ae^{-it};abe^{2iu},ac,ad;q;q)} 並且 x = c o s ( t + u ) {\displaystyle x=cos(t+u)} Remove ads極限關係 連續q哈恩多項式→Q梅西納-帕拉澤克多項式 p n ( c o s ( θ + ϕ ) ; a , 0 , 0 , a ; q ) ( q ; q ) n = P n ( c o s ( θ + ϕ ) ; a | q ) {\displaystyle {\frac {p_{n}(cos(\theta +\phi );a,0,0,a;q)}{(q;q)_{n}}}=P_{n}(cos(\theta +\phi );a|q)} 阿斯基-威爾遜多項式→連續q哈恩多項式 在阿斯基-威爾遜多項式中作代換 θ → θ + ϕ {\displaystyle \theta \to \theta +\phi } , a → a e i θ {\displaystyle a\to ae^{i\theta }} , b → b e i θ {\displaystyle b\to be^{i\theta }} , c → c e − i θ {\displaystyle c\to ce^{-i\theta }} , d → d e − i θ {\displaystyle d\to de^{-i\theta }} 即得連續q哈恩多項式： p n ( c o s ( θ + ϕ ) ; a e i θ , b e i θ , c e − i θ , d e − i θ | q ) = p n ( c o s ( θ + ϕ ) , a , b , c , d ; q ) {\displaystyle p_{n}(cos(\theta +\phi );ae^{i\theta },be^{i\theta },ce^{-i\theta },de^{-i\theta }|q)=p_{n}(cos(\theta +\phi ),a,b,c,d;q)} Remove ads圖集 CONTINUOUS q hahn ABS COMPLEX3D Maple PLOT CONTINUOUS q hahn IIM COMPLEX3D Maple PLOT CONTINUOUS q hahn RE COMPLEX3D Maple PLOT CONTINUOUS q hahn ABS densitu Maple PLOT CONTINUOUS q hahn im densitu Maple PLOT CONTINUOUS q hahn RE densitu Maple PLOT 參考文獻Loading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.Remove ads
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即得連續q哈恩多項式：
