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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Specific values > Specialized values > For fixed lambda, z





http://functions.wolfram.com/07.03.03.0019.01









  


  










Input Form





LaguerreL[10, \[Lambda], z] == (1/3628800) (z^10 - 10 z^9 (10 + \[Lambda]) + 45 z^8 (90 + 19 \[Lambda] + \[Lambda]^2) - 120 z^7 (720 + 242 \[Lambda] + 27 \[Lambda]^2 + \[Lambda]^3) + 210 z^6 (5040 + 2414 \[Lambda] + 431 \[Lambda]^2 + 34 \[Lambda]^3 + \[Lambda]^4) - 252 z^5 (30240 + 19524 \[Lambda] + 5000 \[Lambda]^2 + 635 \[Lambda]^3 + 40 \[Lambda]^4 + \[Lambda]^5) + 210 z^4 (151200 + 127860 \[Lambda] + 44524 \[Lambda]^2 + 8175 \[Lambda]^3 + 835 \[Lambda]^4 + 45 \[Lambda]^5 + \[Lambda]^6) - 120 z^3 (604800 + 662640 \[Lambda] + 305956 \[Lambda]^2 + 77224 \[Lambda]^3 + 11515 \[Lambda]^4 + 1015 \[Lambda]^5 + 49 \[Lambda]^6 + \[Lambda]^7) + 45 z^2 (1814400 + 2592720 \[Lambda] + 1580508 \[Lambda]^2 + 537628 \[Lambda]^3 + 111769 \[Lambda]^4 + 14560 \[Lambda]^5 + 1162 \[Lambda]^6 + 52 \[Lambda]^7 + \[Lambda]^8) - 10 z (3628800 + 6999840 \[Lambda] + 5753736 \[Lambda]^2 + 2655764 \[Lambda]^3 + 761166 \[Lambda]^4 + 140889 \[Lambda]^5 + 16884 \[Lambda]^6 + 1266 \[Lambda]^7 + 54 \[Lambda]^8 + \[Lambda]^9) + 3628800 + 10628640 \[Lambda] + 12753576 \[Lambda]^2 + 8409500 \[Lambda]^3 + 3416930 \[Lambda]^4 + 902055 \[Lambda]^5 + 157773 \[Lambda]^6 + 18150 \[Lambda]^7 + 1320 \[Lambda]^8 + 55 \[Lambda]^9 + \[Lambda]^10)










Standard Form





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MathML Form







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Rule Form





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





2001-10-29