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; }

 MathieuSPrime

 http://functions.wolfram.com/11.04.06.0003.01

 Input Form

 MathieuSPrime[MathieuCharacteristicB[r, q], q, z] \[Proportional] -(r Cos[r z]) + (((2 - r) Cos[(-2 + r) z])/(4 (-1 + r)) + ((2 + r) Cos[(2 + r) z])/(4 (1 + r))) q + (((4 - r) Cos[(-4 + r) z])/(32 (-2 + r) (-1 + r)) + (r (1 + r^2) Cos[r z])/(16 (-1 + r)^2 (1 + r)^2) - ((4 + r) Cos[(4 + r) z])/(32 (1 + r) (2 + r))) q^2 + (((6 - r) Cos[(-6 + r) z])/(384 (-3 + r) (-2 + r) (-1 + r)) + ((-11 - r - r^2 + r^3) Cos[(-2 + r) z])/(128 (-1 + r)^3 (1 + r)^2) - ((11 - r + r^2 + r^3) Cos[(2 + r) z])/(128 (-1 + r)^2 (1 + r)^3) + ((6 + r) Cos[(6 + r) z])/(384 (1 + r) (2 + r) (3 + r))) q^3 + (((8 - r) Cos[(-8 + r) z])/(6144 (-4 + r) (-3 + r) (-2 + r) (-1 + r)) + ((-4 + r) (-29 - 7 r - r^2 + r^3) Cos[(-4 + r) z])/ (1536 (-3 + r) (-2 + r) (-1 + r)^3 (1 + r)^2) - (r (316 + 675 r^2 - 185 r^4 - 15 r^6 + r^8) Cos[r z])/ (1024 (-2 + r)^2 (-1 + r)^4 (1 + r)^4 (2 + r)^2) + ((4 + r) (29 - 7 r + r^2 + r^3) Cos[(4 + r) z])/ (1536 (-1 + r)^2 (1 + r)^3 (2 + r) (3 + r)) - ((8 + r) Cos[(8 + r) z])/(6144 (1 + r) (2 + r) (3 + r) (4 + r))) q^4 + (((10 - r) Cos[(-10 + r) z])/(122880 (-5 + r) (-4 + r) (-3 + r) (-2 + r) (-1 + r)) + ((-6 + r) (-55 - 17 r - r^2 + r^3) Cos[(-6 + r) z])/ (24576 (-4 + r) (-3 + r) (-2 + r) (-1 + r)^3 (1 + r)^2) - ((-7564 - 3572 r - 6335 r^2 + 1931 r^3 + 2457 r^4 - 273 r^5 - 5 r^6 - 31 r^7 - r^8 + r^9) Cos[(-2 + r) z])/(12288 (-3 + r) (-2 + r) (-1 + r)^5 (1 + r)^4 (2 + r)^2) + ((7564 - 3572 r + 6335 r^2 + 1931 r^3 - 2457 r^4 - 273 r^5 + 5 r^6 - 31 r^7 + r^8 + r^9) Cos[(2 + r) z])/(12288 (-2 + r)^2 (-1 + r)^4 (1 + r)^5 (2 + r) (3 + r)) - ((6 + r) (55 - 17 r + r^2 + r^3) Cos[(6 + r) z])/(24576 (-1 + r)^2 (1 + r)^3 (2 + r) (3 + r) (4 + r)) + ((10 + r) Cos[(10 + r) z])/(122880 (1 + r) (2 + r) (3 + r) (4 + r) (5 + r))) q^5 + (((12 - r) Cos[(-12 + r) z])/ (2949120 (-6 + r) (-5 + r) (-4 + r) (-3 + r) (-2 + r) (-1 + r)) + ((-8 + r) (-89 - 31 r - r^2 + r^3) Cos[(-8 + r) z])/ (491520 (-5 + r) (-4 + r) (-3 + r) (-2 + r) (-1 + r)^3 (1 + r)^2) - ((71528 + 16404 r + 32954 r^2 - 32025 r^3 - 16879 r^4 + 8211 r^5 + 145 r^6 + 69 r^7 - 53 r^8 - 3 r^9 + r^10) Cos[(-4 + r) z])/ (196608 (-3 + r) (-2 + r)^3 (-1 + r)^5 (1 + r)^4 (2 + r)^2) + (r (1329084 + 4883287 r^2 + 153312 r^4 - 718317 r^6 + 75244 r^8 + 597 r^10 - 72 r^12 + r^14) Cos[r z])/(147456 (-3 + r)^2 (-2 + r)^2 (-1 + r)^6 (1 + r)^6 (2 + r)^2 (3 + r)^2) - ((71528 - 16404 r + 32954 r^2 + 32025 r^3 - 16879 r^4 - 8211 r^5 + 145 r^6 - 69 r^7 - 53 r^8 + 3 r^9 + r^10) Cos[(4 + r) z])/ (196608 (-2 + r)^2 (-1 + r)^4 (1 + r)^5 (2 + r)^3 (3 + r)) + ((8 + r) (89 - 31 r + r^2 + r^3) Cos[(8 + r) z])/ (491520 (-1 + r)^2 (1 + r)^3 (2 + r) (3 + r) (4 + r) (5 + r)) - ((12 + r) Cos[(12 + r) z])/(2949120 (1 + r) (2 + r) (3 + r) (4 + r) (5 + r) (6 + r))) q^6 + SeriesData[\$CellContext`q, 0, {}, 0, 7, 1] /; !(Element[r, Integers] && -6 <= r <= 6)

 Standard Form

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 MathML Form

 Se ( b MathieuCharacteristicB r ( q ) , q , z ) - r cos ( r z ) + ( ( 2 - r ) cos ( ( r - 2 ) z ) 4 ( r - 1 ) + ( r + 2 ) cos ( ( r + 2 ) z ) 4 ( r + 1 ) ) q + ( ( 4 - r ) cos ( ( r - 4 ) z ) 32 ( r - 2 ) ( r - 1 ) + r ( r 2 + 1 ) cos ( r z ) 16 ( r - 1 ) 2 ( r + 1 ) 2 - ( r + 4 ) cos ( ( r + 4 ) z ) 32 ( r + 1 ) ( r + 2 ) ) q 2 + ( ( 6 - r ) cos ( ( r - 6 ) z ) 384 ( r - 3 ) ( r - 2 ) ( r - 1 ) + ( ( r 3 - r 2 - r - 11 ) cos ( ( r - 2 ) z ) ) / ( 128 ( r - 1 ) 3 ( r + 1 ) 2 ) - ( ( r 3 + r 2 - r + 11 ) cos ( ( r + 2 ) z ) ) / ( 128 ( r - 1 ) 2 ( r + 1 ) 3 ) + ( ( r + 6 ) cos ( ( r + 6 ) z ) ) / ( 384 ( r + 1 ) ( r + 2 ) ( r + 3 ) ) ) q 3 + ( ( ( 8 - r ) cos ( ( r - 8 ) z ) ) / ( 6144 ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) ) + ( ( r - 4 ) ( r 3 - r 2 - 7 r - 29 ) cos ( ( r - 4 ) z ) ) / ( 1536 ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 ) - ( r ( r 8 - 15 r 6 - 185 r 4 + 675 r 2 + 316 ) cos ( r z ) ) / ( 1024 ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 4 ( r + 2 ) 2 ) + ( ( r + 4 ) ( r 3 + r 2 - 7 r + 29 ) cos ( ( r + 4 ) z ) ) / ( 1536 ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) ) - ( ( r + 8 ) cos ( ( r + 8 ) z ) ) / ( 6144 ( r + 1 ) ( r + 2 ) ( r + 3 ) ( r + 4 ) ) ) q 4 + ( ( ( 10 - r ) cos ( ( r - 10 ) z ) ) / ( 122880 ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) ) + ( ( r - 6 ) ( r 3 - r 2 - 17 r - 55 ) cos ( ( r - 6 ) z ) ) / ( 24576 ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 ) - ( ( 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 ) cos ( ( r - 2 ) z ) ) / ( 12288 ( r - 3 ) ( r - 2 ) ( r - 1 ) 5 ( r + 1 ) 4 ( r + 2 ) 2 ) + ( ( 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 ) cos ( ( r + 2 ) z ) ) / ( 12288 ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 5 ( r + 2 ) ( r + 3 ) ) - ( ( r + 6 ) ( r 3 + r 2 - 17 r + 55 ) cos ( ( r + 6 ) z ) ) / ( 24576 ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) ( r + 4 ) ) + ( ( r + 10 ) cos ( ( r + 10 ) z ) ) / ( 122880 ( r + 1 ) ( r + 2 ) ( r + 3 ) ( r + 4 ) ( r + 5 ) ) ) q 5 + ( ( ( 12 - r ) cos ( ( r - 12 ) z ) ) / ( 2949120 ( r - 6 ) ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) ) + ( ( r - 8 ) ( r 3 - r 2 - 31 r - 89 ) cos ( ( r - 8 ) z ) ) / ( 491520 ( r - 5 ) ( r - 4 ) ( r - 3 ) ( r - 2 ) ( r - 1 ) 3 ( r + 1 ) 2 ) - ( ( 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 ) cos ( ( r - 4 ) z ) ) / ( 196608 ( r - 3 ) ( r - 2 ) 3 ( r - 1 ) 5 ( r + 1 ) 4 ( r + 2 ) 2 ) + ( r ( r 14 - 72 r 12 + 597 r 10 + 75244 r 8 - 718317 r 6 + 153312 r 4 + 4883287 r 2 + 1329084 ) cos ( r z ) ) / ( 147456 ( r - 3 ) 2 ( r - 2 ) 2 ( r - 1 ) 6 ( r + 1 ) 6 ( r + 2 ) 2 ( r + 3 ) 2 ) - ( ( 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 ) cos ( ( r + 4 ) z ) ) / ( 196608 ( r - 2 ) 2 ( r - 1 ) 4 ( r + 1 ) 5 ( r + 2 ) 3 ( r + 3 ) ) + ( ( r + 8 ) ( r 3 + r 2 - 31 r + 89 ) cos ( ( r + 8 ) z ) ) / ( 491520 ( r - 1 ) 2 ( r + 1 ) 3 ( r + 2 ) ( r + 3 ) ( r 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 Rule Form

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

 2001-10-29