html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 MathieuS

 http://functions.wolfram.com/11.02.06.0003.01

 Input Form

 MathieuS[MathieuCharacteristicB[r, q], q, z] \[Proportional] Sin[r z] + (1/4) (Sin[(r - 2) z]/(r - 1) - Sin[(r + 2) z]/(r + 1)) q + (1/32) (Sin[(r - 4) z]/((r - 2) (r - 1)) - (2 (r^2 + 1) Sin[r z])/ ((r - 1)^2 (r + 1)^2) + Sin[(r + 4) z]/((r + 1) (r + 2))) q^2 + (1/384) (Sin[(r - 6) z]/((r - 3) (r - 2) (r - 1)) - (3 (r^3 - r^2 - r - 11) Sin[(r - 2) z])/((r - 2) (r - 1)^3 (r + 1)^2) + (3 (r^3 + r^2 - r + 11) Sin[(r + 2) z])/((r - 1)^2 (r + 1)^3 (r + 2)) - Sin[(r + 6) z]/((r + 1) (r + 2) (r + 3))) q^3 + (1/6144) (Sin[(r - 8) z]/((r - 4) (r - 3) (r - 2) (r - 1)) - (4 (r^3 - r^2 - 7 r - 29) Sin[(r - 4) z])/((r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (6 (r^8 - 15 r^6 - 185 r^4 + 675 r^2 + 316) Sin[r z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^4 (r + 2)^2) - (4 (r^3 + r^2 - 7 r + 29) Sin[(r + 4) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3)) + Sin[(r + 8) z]/((r + 1) (r + 2) (r + 3) (r + 4))) q^4 + (1/122880) (Sin[(r - 10) z]/((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (5 (r^3 - r^2 - 17 r - 55) Sin[(r - 6) z])/((r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (10 (r^9 - r^8 - 31 r^7 - 5 r^6 - 273 r^5 + 2457 r^4 + 1931 r^3 - 6335 r^2 - 3572 r - 7564) Sin[(r - 2) z])/ ((r - 3) (r - 2)^2 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (10 (r^9 + r^8 - 31 r^7 + 5 r^6 - 273 r^5 - 2457 r^4 + 1931 r^3 + 6335 r^2 - 3572 r + 7564) Sin[(r + 2) z])/((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^2 (r + 3)) + (5 (r^3 + r^2 - 17 r + 55) Sin[(r + 6) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4)) - Sin[(r + 10) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5))) q^5 + (1/2949120) (Sin[(r - 12) z]/((r - 6) (r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (6 (r^3 - r^2 - 31 r - 89) Sin[(r - 8) z])/ ((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (15 (r^10 - 3 r^9 - 53 r^8 + 69 r^7 + 145 r^6 + 8211 r^5 - 16879 r^4 - 32025 r^3 + 32954 r^2 + 16404 r + 71528) Sin[(r - 4) z])/ ((r - 4) (r - 3) (r - 2)^3 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (20 (r^14 - 72 r^12 + 597 r^10 + 75244 r^8 - 718317 r^6 + 153312 r^4 + 4883287 r^2 + 1329084) Sin[r z])/((r - 3)^2 (r - 2)^2 (r - 1)^6 (r + 1)^6 (r + 2)^2 (r + 3)^2) + (15 (r^10 + 3 r^9 - 53 r^8 - 69 r^7 + 145 r^6 - 8211 r^5 - 16879 r^4 + 32025 r^3 + 32954 r^2 - 16404 r + 71528) Sin[(r + 4) z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^3 (r + 3) (r + 4)) - (6 (r^3 + r^2 - 31 r + 89) Sin[(r + 8) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4) (r + 5)) + Sin[(r + 12) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5) (r + 6))) q^6 + O[q]^7 /; !(Element[r, Integers] && -6 <= r <= 6)

 Standard Form

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 MathML Form

 Se ( b r ( q ) , q , z ) sin ( r z ) + 1 4 ( sin ( ( r - 2 ) z ) r - 1 - sin ( ( r + 2 ) z ) r + 1 ) q + 1 32 ( sin ( ( r - 4 ) z ) ( r - 2 ) ( r - 1 ) - 2 ( r 2 + 1 ) sin ( r z ) ( r - 1 ) 2 ( r + 1 ) 2 + sin ( ( r + 4 ) z ) ( r + 1 ) ( r + 2 ) ) q 2 + 1 384 ( sin ( ( r - 6 ) z ) ( r - 3 ) ( r - 2 ) ( r - 1 ) - 3 ( r 3 - r 2 - r - 11 ) sin ( ( r - 2 ) z ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 + 3 ( r 3 + r 2 - r + 11 ) sin ( ( r + 2 ) z ) ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) - sin ( ( r + 6 ) z ) ( r + 1 ) ( r + 2 ) ( r + 3 ) ) q 3 + 1 6144 ( sin ( ( r - 8 ) z ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) - 4 ( r 3 - r 2 - 7 r - 29 ) sin ( ( r - 4 ) z ) ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 + 6 ( r 8 - 15 r 6 - 185 r 4 + 675 r 2 + 316 ) sin ( r z ) ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 4 ( r + 2 ) 2 - 4 ( r 3 + r 2 - 7 r + 29 ) sin ( ( r + 4 ) z ) ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) + sin ( ( r + 8 ) z ) ( r + 1 ) ( r + 2 ) ( r + 3 ) ( r + 4 ) ) q 4 + 1 122880 ( sin ( ( r - 10 ) z ) ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) - 5 ( r 3 - r 2 - 17 r - 55 ) sin ( ( r - 6 ) z ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 + ( 10 ( r 9 - r 8 - 31 r 7 - 5 r 6 - 273 r 5 + 2457 r 4 + 1931 r 3 - 6335 r 2 - 3572 r - 7564 ) sin ( ( r - 2 ) z ) ) / ( ( r - 3 ) ( r - 2 ) 2 ( r - 1 ) 5 ( r + 1 ) 4 ( r + 2 ) 2 ) - ( 10 ( r 9 + r 8 - 31 r 7 + 5 r 6 - 273 r 5 - 2457 r 4 + 1931 r 3 + 6335 r 2 - 3572 r + 7564 ) sin ( ( r + 2 ) z ) ) / ( ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 5 ( r + 2 ) 2 ( r + 3 ) ) + 5 ( r 3 + r 2 - 17 r + 55 ) sin ( ( r + 6 ) z ) ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) ( r + 4 ) - sin ( ( r + 10 ) z ) ( r + 1 ) ( r + 2 ) ( r + 3 ) ( r + 4 ) ( r + 5 ) ) q 5 + 1 2949120 ( sin ( ( r - 12 ) z ) ( r - 6 ) ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) - 6 ( r 3 - r 2 - 31 r - 89 ) sin ( ( r - 8 ) z ) ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 + ( 15 ( r 10 - 3 r 9 - 53 r 8 + 69 r 7 + 145 r 6 + 8211 r 5 - 16879 r 4 - 32025 r 3 + 32954 r 2 + 16404 r + 71528 ) sin ( ( r - 4 ) z ) ) / ( ( r - 4 ) ( r - 3 ) ( r - 2 ) 3 ( r - 1 ) 5 ( r + 1 ) 4 ( r + 2 ) 2 ) - ( 20 ( r 14 - 72 r 12 + 597 r 10 + 75244 r 8 - 718317 r 6 + 153312 r 4 + 4883287 r 2 + 1329084 ) sin ( r z ) ) / ( ( r - 3 ) 2 ( r - 2 ) 2 ( r - 1 ) 6 ( r + 1 ) 6 ( r + 2 ) 2 ( r + 3 ) 2 ) + ( 15 ( r 10 + 3 r 9 - 53 r 8 - 69 r 7 + 145 r 6 - 8211 r 5 - 16879 r 4 + 32025 r 3 + 32954 r 2 - 16404 r + 71528 ) sin ( ( r + 4 ) z ) ) / ( ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 5 ( r + 2 ) 3 ( r + 3 ) ( r + 4 ) ) - 6 ( r 3 + r 2 - 31 r + 89 ) sin ( ( r + 8 ) z ) ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) ( r + 4 ) ( r + 5 ) + sin ( ( r + 12 ) z ) ( r + 1 ) ( r + 2 ) ( r + 3 ) ( r + 4 ) ( r + 5 ) ( r + 6 ) ) q 6 + O ( q 7 ) /; ¬ ( r TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] - 6 r 6 ) Condition Proportional Se Subscript b r q q z r z 1 4 r -2 z r -1 -1 -1 r 2 z r 1 -1 q 1 32 r -4 z r -2 r -1 -1 -1 2 r 2 1 r z r -1 2 r 1 2 -1 r 4 z r 1 r 2 -1 q 2 1 384 r -6 z r -3 r -2 r -1 -1 -1 3 r 3 -1 r 2 -1 r -11 r -2 z r -2 r -1 3 r 1 2 -1 3 r 3 r 2 -1 r 11 r 2 z r -1 2 r 1 3 r 2 -1 -1 r 6 z r 1 r 2 r 3 -1 q 3 1 6144 r -8 z r -4 r -3 r -2 r -1 -1 -1 4 r 3 -1 r 2 -1 7 r -29 r -4 z r -3 r -2 r -1 3 r 1 2 -1 6 r 8 -1 15 r 6 -1 185 r 4 675 r 2 316 r z r -2 2 r -1 4 r 1 4 r 2 2 -1 -1 4 r 3 r 2 -1 7 r 29 r 4 z r -1 2 r 1 3 r 2 r 3 -1 r 8 z r 1 r 2 r 3 r 4 -1 q 4 1 122880 r -10 z r -5 r -4 r -3 r -2 r -1 -1 -1 5 r 3 -1 r 2 -1 17 r -55 r -6 z r -4 r -3 r -2 r -1 3 r 1 2 -1 10 r 9 -1 r 8 -1 31 r 7 -1 5 r 6 -1 273 r 5 2457 r 4 1931 r 3 -1 6335 r 2 -1 3572 r -7564 r -2 z r -3 r -2 2 r -1 5 r 1 4 r 2 2 -1 -1 10 r 9 r 8 -1 31 r 7 5 r 6 -1 273 r 5 -1 2457 r 4 1931 r 3 6335 r 2 -1 3572 r 7564 r 2 z r -2 2 r -1 4 r 1 5 r 2 2 r 3 -1 5 r 3 r 2 -1 17 r 55 r 6 z r -1 2 r 1 3 r 2 r 3 r 4 -1 -1 r 10 z r 1 r 2 r 3 r 4 r 5 -1 q 5 1 2949120 r -12 z r -6 r -5 r -4 r -3 r -2 r -1 -1 -1 6 r 3 -1 r 2 -1 31 r -89 r -8 z r -5 r -4 r -3 r -2 r -1 3 r 1 2 -1 15 r 10 -1 3 r 9 -1 53 r 8 69 r 7 145 r 6 8211 r 5 -1 16879 r 4 -1 32025 r 3 32954 r 2 16404 r 71528 r -4 z r -4 r -3 r -2 3 r -1 5 r 1 4 r 2 2 -1 -1 20 r 14 -1 72 r 12 597 r 10 75244 r 8 -1 718317 r 6 153312 r 4 4883287 r 2 1329084 r z r -3 2 r -2 2 r -1 6 r 1 6 r 2 2 r 3 2 -1 15 r 10 3 r 9 -1 53 r 8 -1 69 r 7 145 r 6 -1 8211 r 5 -1 16879 r 4 32025 r 3 32954 r 2 -1 16404 r 71528 r 4 z r -2 2 r -1 4 r 1 5 r 2 3 r 3 r 4 -1 -1 6 r 3 r 2 -1 31 r 89 r 8 z r -1 2 r 1 3 r 2 r 3 r 4 r 5 -1 r 12 z r 1 r 2 r 3 r 4 r 5 r 6 -1 q 6 O q 7 r -6 r 6 [/itex]

 Rule Form

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

 2001-10-29