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JacobiZeta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.07.06.0002.02









  


  










Input Form





JacobiZeta[z, m] \[Proportional] (1/4) m Sin[2 z] + m^2 ((1/16) Sin[2 z] - (1/64) Sin[4 z]) + m^3 ((17/512) Sin[2 z] - (3/256) Sin[4 z] + (1/512) Sin[6 z]) + m^4 ((45 Sin[2 z])/2048 - (37 Sin[4 z])/4096 + (5 Sin[6 z])/2048 - (5 Sin[8 z])/16384) + m^5 ((1059 Sin[2 z])/65536 - (119 Sin[4 z])/16384 + (325 Sin[6 z])/131072 - (35 Sin[8 z])/65536 + (7 Sin[10 z])/131072) + m^6 ((3315 Sin[2 z])/262144 - (12653 Sin[4 z])/2097152 + (1245 Sin[6 z])/524288 - (707 Sin[8 z])/1048576 + (63 Sin[10 z])/524288 - (21 Sin[12 z])/2097152) + m^7 ((172989 Sin[2 z])/16777216 - (43087 Sin[4 z])/8388608 + (37377 Sin[6 z])/16777216 - (3157 Sin[8 z])/4194304 + (3045 Sin[10 z])/16777216 - (231 Sin[12 z])/8388608 + (33 Sin[14 z])/16777216) + O[m^8] /; (m -> 0)










Standard Form





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MathML Form







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type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 1048576 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12653 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2097152 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2097152 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 172989 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16777216 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 37377 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16777216 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3045 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16777216 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16777216 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3157 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4194304 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 43087 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 8388608 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 231 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 8388608 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.