Inverse of the regularized incomplete gamma function: Series representations (formula 06.12.06.0005)

InverseGammaRegularized

$Mathematica Notation$

Gamma, Beta, Erf

InverseGammaRegularized[a,z]

Series representations

Generalized power series

Expansions at generic point z==z₀

For the function itself

http://functions.wolfram.com/06.12.06.0005.01

Input Form

InverseGammaRegularized[a, z] \[Proportional] InverseGammaRegularized[a, Subscript[z, 0]] - E^w w^(1 - a) Gamma[a] (z - Subscript[z, 0]) + (1/2) E^(2 w) w^(1 - 2 a) (1 - a + w) Gamma[a]^2 (z - Subscript[z, 0])^2 - (1/6) E^(3 w) w^(1 - 3 a) (1 + 2 a^2 + 2 w (2 + w) - a (3 + 4 w)) Gamma[a]^3 (z - Subscript[z, 0])^3 + (1/24) E^(4 w) w^(1 - 4 a) (1 - 6 a^3 + a^2 (11 + 18 w) + w (11 + 6 w (3 + w)) - a (6 + w (29 + 18 w))) Gamma[a]^4 (z - Subscript[z, 0])^4 - (1/120) E^(5 w) w^(1 - 5 a) (1 + 24 a^4 - 2 a^3 (25 + 48 w) + 2 w (1 + w) (13 + 12 w (3 + w)) + a^2 (35 + 4 w (49 + 36 w)) - 2 a (5 + w (63 + w (121 + 48 w)))) Gamma[a]^5 (z - Subscript[z, 0])^5 + (1/720) E^(6 w) w^(1 - 6 a) (1 - 120 a^5 + a^4 (274 + 600 w) - 3 a^3 (75 + 474 w + 400 w^2) + a^2 (85 + 3 w (399 + 874 w + 400 w^2)) + w (57 + 2 w (212 + w (437 + 60 w (5 + w)))) - a (15 + 2 w (216 + w (923 + w (1037 + 300 w))))) Gamma[a]^6 (z - Subscript[z, 0])^6 - (1/5040) E^(7 w) w^(1 - 7 a) (1 + a (-21 + a (175 + a (-735 + 4 a (406 + 9 a (-49 + 20 a))))) + 120 w - 24 a (54 + a (-229 + 6 a (79 + a (-79 + 30 a)))) w + 6 (-1 + a) (-1 + 2 a) (269 + 36 a (-27 + 25 a)) w^2 - 8 (-1 + a) (755 + 18 a (-129 + 100 a)) w^3 + 36 (-1 + a) (-229 + 300 a) w^4 - 4320 (-1 + a) w^5 + 720 w^6) Gamma[a]^7 (z - Subscript[z, 0])^7 + (1/40320) E^(8 w) w^(1 - 8 a) (1 - 28 a + 322 a^2 - 1960 a^3 + 6769 a^4 - 13132 a^5 + 13068 a^6 - 5040 a^7 + (-1 + a) (-1 + 2 a) (-1 + 3 a) (-247 + a (2097 + 10 a (-599 + 588 a))) w - 6 (-1 + a) (-1 + 2 a) (-947 + a (5891 + 60 a (-206 + 147 a))) w^2 + 2 (-1 + a) (-17729 + 2 a (45001 + 90 a (-853 + 490 a))) w^3 - 20 (-1 + a) (4175 + 9 a (-1343 + 980 a)) w^4 + 36 (-1 + a) (-2323 + 2940 a) w^5 - 35280 (-1 + a) w^6 + 5040 w^7) Gamma[a]^8 (z - Subscript[z, 0])^8 + \[Ellipsis] /; (z -> Subscript[z, 0]) && w = InverseGammaRegularized[a, Subscript[z, 0]]

Standard Form

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MathML Form

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<msup> <mi> ⅇ </mi> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <mtext> </mtext> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 18 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 18 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mtext> </mtext> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 120 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 25 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 49 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 121 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 63 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 13 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 720 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 120 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 600 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 274 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 474 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 75 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 874 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 399 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 85 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 300 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1037 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 923 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 216 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 437 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 212 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 57 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 5040 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 720 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4320 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 300 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 229 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 18 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 100 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 129 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 755 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 27 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 269 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 79 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 79 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 229 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 54 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mn> 120 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 49 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 406 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 735 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 7 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 7 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 40320 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 5040 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13068 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13132 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6769 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1960 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 322 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 5040 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 35280 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2940 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 2323 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 980 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1343 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4175 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 490 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 853 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45001 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 17729 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 147 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 206 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5891 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 947 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 588 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 599 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2097 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 247 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mi> w </mi> </mrow> </mrow> <mo> = </mo> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Set </ci> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> w </ci> </apply> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> w </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> w </ci> </apply> <cn type='integer'> 3 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 24 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -6 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> w </ci> </apply> <cn type='integer'> 11 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> w </ci> </apply> <cn type='integer'> 29 </cn> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 120 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 48 </cn> <ci> w </ci> </apply> <cn type='integer'> 25 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 36 </cn> <ci> w </ci> </apply> <cn type='integer'> 49 </cn> </apply> </apply> <cn type='integer'> 35 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 48 </cn> <ci> w </ci> </apply> <cn type='integer'> 121 </cn> </apply> </apply> <cn type='integer'> 63 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 13 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 720 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -120 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 600 </cn> <ci> w </ci> </apply> <cn type='integer'> 274 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 474 </cn> <ci> w </ci> </apply> <cn type='integer'> 75 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 874 </cn> <ci> w </ci> </apply> <cn type='integer'> 399 </cn> </apply> </apply> <cn type='integer'> 85 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 300 </cn> <ci> w </ci> </apply> <cn type='integer'> 1037 </cn> </apply> </apply> <cn type='integer'> 923 </cn> </apply> </apply> <cn type='integer'> 216 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> 437 </cn> </apply> </apply> <cn type='integer'> 212 </cn> </apply> </apply> <cn type='integer'> 57 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 5040 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 720 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4320 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 300 </cn> <ci> a </ci> </apply> <cn type='integer'> -229 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 100 </cn> <ci> a </ci> </apply> <cn type='integer'> -129 </cn> </apply> </apply> <cn type='integer'> 755 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 36 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 25 </cn> <ci> a </ci> </apply> <cn type='integer'> -27 </cn> </apply> </apply> <cn type='integer'> 269 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 30 </cn> <ci> a </ci> </apply> <cn type='integer'> -79 </cn> </apply> </apply> <cn type='integer'> 79 </cn> </apply> </apply> <cn type='integer'> -229 </cn> </apply> </apply> <cn type='integer'> 54 </cn> </apply> <ci> w </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 120 </cn> <ci> w </ci> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 20 </cn> <ci> a </ci> </apply> <cn type='integer'> -49 </cn> </apply> </apply> <cn type='integer'> 406 </cn> </apply> </apply> <cn type='integer'> -735 </cn> </apply> </apply> <cn type='integer'> 175 </cn> </apply> </apply> <cn type='integer'> -21 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 40320 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -5040 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13068 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13132 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6769 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1960 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 322 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 28 </cn> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 5040 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35280 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Rule Form

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

2007-05-02

InverseGammaRegularized[a,z₁,z₂]