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MathieuCPrime






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuCPrime[a,q,z] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.03.06.0009.01









  


  










Input Form





MathieuCPrime[MathieuCharacteristicA[5, q], q, z] \[Proportional] -(5 Sin[5 z]) + ((-(3/16)) Sin[3 z] + (7/24) Sin[7 z]) q + (-(Sin[z]/384) + (65 Sin[5 z])/4608 - (3/448) Sin[9 z]) q^2 + (-(Sin[z]/9216) + (7 Sin[3 z])/24576 - (13 Sin[7 z])/36864 + (11 Sin[11 z])/129024) q^3 + (Sin[z]/589824 - Sin[3 z]/49152 - (4015 Sin[5 z])/2080899072 + Sin[9 z]/229376 - (13 Sin[13 z])/18579456) q^4 + (-((5 Sin[z])/42467328) + (457 Sin[3 z])/11098128384 + (25 Sin[5 z])/7077888 - (1157 Sin[7 z])/7134511104 - (55 Sin[11 z])/1783627776 + Sin[15 z]/247726080) q^5 + (-((3407 Sin[z])/799065243648) + (49 Sin[3 z])/226492416 + (9145 Sin[5 z])/456608710656 - (7 Sin[7 z])/56623104 + (1273 Sin[9 z])/310747594752 + (13 Sin[13 z])/101921587200 - (17 Sin[17 z])/980995276800) q^6 + ((71521 Sin[z])/19177565847552 + (2237 Sin[3 z])/17046725197824 - (205 Sin[5 z])/10871635968 - (263827 Sin[7 z])/230130790170624 + (5 Sin[9 z])/2466250752 - (953513 Sin[11 z])/20136444139929600 - Sin[15 z]/4185579847680 + (19 Sin[19 z])/329614413004800) q^7 + ((718283 Sin[z])/3682092642729984 - (64811 Sin[3 z])/102280351186944 + (755718235 Sin[5 z])/2886760631900307456 + (3161 Sin[7 z])/5479304527872 + (294521 Sin[9 z])/11932707638476800 - (253 Sin[11 z])/12785043898368 + (3609307 Sin[13 z])/ 10632042505882828800 - (17 Sin[17 z])/31642983648460800 - Sin[21 z]/6529504562380800) q^8 + (-((187567 Sin[z])/29456741141839872) + (889319687 Sin[3 z])/ 15396056703468306432 + (7955 Sin[5 z])/424274049368064 - (10349972261 Sin[7 z])/742309876774364774400 - (157 Sin[9 z])/17046725197824 - (27393431 Sin[11 z])/ 92788734596795596800 + (715 Sin[13 z])/5523138964094976 - (9607 Sin[15 z])/5670422669804175360 + (19 Sin[19 z])/ 3290870299439923200 + (23 Sin[23 z])/69108276288238387200) q^9 + ((1135692325 Sin[z])/3325548247949154189312 + (592465 Sin[3 z])/ 1099718335962021888 - (18970709026319 Sin[5 z])/ 1662774123974577094656000 - (13721 Sin[7 z])/117826964567359488 + (21353891011 Sin[9 z])/71129781970023575715840 + (6919 Sin[11 z])/75745905793302528 + (112350719 Sin[13 z])/ 48992451867108075110400 - (1123 Sin[15 z])/1841046321364992000 + (187 Sin[17 z])/29784038265638092800 - Sin[21 z]/42123139832831016960 - Sin[25 z]/1658598630917721292800) q^10 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]










Standard Form





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MathML Form







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</mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 384 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 65 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4608 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 448 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) 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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998- Wolfram Research, Inc.