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JacobiAmplitude






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/09.24.06.0008.01









  


  










Input Form





JacobiAmplitude[z, m] \[Proportional] z - (m z^3)/6 + (1/120) (4 m + m^2) z^5 - ((16 m + 44 m^2 + m^3) z^7)/5040 + ((64 m + 912 m^2 + 408 m^3 + m^4) z^9)/362880 - ((256 m + 15808 m^2 + 30768 m^3 + 3688 m^4 + m^5) z^11)/39916800 + ((1024 m + 259328 m^2 + 1538560 m^3 + 870640 m^4 + 33212 m^5 + m^6) z^13)/ 6227020800 - (1/1307674368000) ((4096 m + 4180992 m^2 + 65008896 m^3 + 106923008 m^4 + 22945056 m^5 + 298932 m^6 + m^7) z^15) + (1/355687428096000) ((m^8 + 2690416 m^7 + 586629984 m^6 + 6337665152 m^5 + 9860488448 m^4 + 2536974336 m^3 + 67047424 m^2 + 16384 m) z^17) - ((m^9 + 24213776 m^8 + 14804306080 m^7 + 345558617984 m^6 + 1165333452544 m^5 + 782931974144 m^4 + 95153582080 m^3 + 1073463296 m^2 + 65536 m) z^19)/121645100408832000 + O[z^11]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.