DLMF:18.11.E3 (Q5637): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10922 / rank
 
Normal rank
Property / Symbols used: Q10922 / qualifier
 
test:

H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}

\HermitepolyH{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10922 / qualifier
 
xml-id: C18.S3.T1.t1.r13.m2adec
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
test:

U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E6.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
test:

U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

\paraU@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11320 / qualifier
 
xml-id: C12.S2.SS1.p1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1bdec

Latest revision as of 14:29, 2 January 2020

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DLMF:18.11.E3
No description defined

    Statements

    test
    H n ⁡ ( x ) = 2 n ⁢ U ⁡ ( - 1 2 ⁢ n , 1 2 , x 2 ) = 2 n ⁢ x ⁢ U ⁡ ( - 1 2 ⁢ n + 1 2 , 3 2 , x 2 ) = 2 1 2 ⁢ n ⁢ e 1 2 ⁢ x 2 ⁢ U ⁡ ( - n - 1 2 , 2 1 2 ⁢ x ) . Hermite-polynomial-H 𝑛 𝑥 superscript 2 𝑛 Kummer-confluent-hypergeometric-U 1 2 𝑛 1 2 superscript 𝑥 2 superscript 2 𝑛 𝑥 Kummer-confluent-hypergeometric-U 1 2 𝑛 1 2 3 2 superscript 𝑥 2 superscript 2 1 2 𝑛 superscript 𝑒 1 2 superscript 𝑥 2 parabolic-U 𝑛 1 2 superscript 2 1 2 𝑥 {\displaystyle{\displaystyle H_{n}\left(x\right)=2^{n}U\left(-\tfrac{1}{2}n,% \tfrac{1}{2},x^{2}\right)=2^{n}xU\left(-\tfrac{1}{2}n+\tfrac{1}{2},\tfrac{3}{2% },x^{2}\right)=2^{\frac{1}{2}n}e^{\frac{1}{2}x^{2}}U\left(-n-\tfrac{1}{2},2^{% \frac{1}{2}}x\right).}}
    0 references
    DLMF id
    DLMF:18.11.E3
    0 references
    Symbols used
    Q10922
    test
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2adec
    0 references
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q11320
    test
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
     
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