| Jan 1, 2017 - New Year's Day |  |
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Hello, PLANETQUANTUM.COM visitor. :-) Happy New Year to you and wishing you much success in 2017. Let's test some q-function identities mentioned in István Mezö, "Several special values of Jacobi theta functions" https://arxiv.org/pdf/1106.2703.pdf . C:\Temp>qconsole >(SetPrecision 150) 150 >(Setq q (Random)) .355137292830204446040446680586593508063560573 >(Setq z (Random)) .203417555285391595827949454245639793772563901 >(QCos q z) .979381891475308569875632622475047204341036211 >(QSin q (- (/ _Pi 2) z)) .979381891475308569875632622475047204341036211 >(QSin q (* 2 z)) .395704743499764397816126636850458208601633875 >(* (^ q -1/4) (^ (QPochhammer (^ q 2) (^ q 4) _Infinity) 4) (^ (QPochhammer q (^ q 2) _Infinity) -2) (QSin (^ q 2) z) (QCos (^ q 2) z)) .395704743499764397816126636850458208601633876 >(QSin q (* 2 z)) .395704743499764397816126636850458208601633875 >(* (^ q -1/4) (/ (^ (QEuler (^ q 2)) 6) (* (^ (QEuler q) 2) (^ (QEuler (^ q 4)) 4))) (QSin (^ q 2) z) (QCos (^ q 2) z)) .395704743499764397816126636850458208601633875 >(QCos q (* 2 z)) .918377778967351404206934515211872228766801206 >(- (^ (QCos (^ q 2) z) 2) (^ (QSin (^ q 2) z) 2)) .918377778967351404206934515211872228766801206 >(QSin q z) .202017591730828019212444730769624786518875034 >(* (^ q 1/4) (^ (QGamma (^ q 2) 1/2) 2) (/ (^ (^ q 2) (Binomial (/ z _Pi) 2)) (* (QGamma (^ q 2) (/ z _Pi)) (QGamma (^ q 2) (- 1 (/ z _Pi)))))) .202017591730828019212444730769624786518875042 >(QSin (^ q 2) (/ _Pi 4)) .707004423594506121995272278335598201755934937 >(Def (C q) (* (^ q -1/4) (/ (^ (QEuler (^ q 2)) 6) (* (^ (QEuler q) 2) (^ (QEuler (^ q 4)) 4)))) ) C >(^ (C q) -1/2) .707004423594506121995272278335598201755934937 >(QSin (^ q 2) (/ _Pi 8)) .382588866281506265790050905283644236435230184 >(Sqrt (* (QSin q (/ _Pi 4)) (/ (- (Sqrt (+ 1 (/ 4 (^ (C q) 2)))) 1) 2))) .382588866281506265790050905283644236435230184 >
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