DLMF:12.7.E7 (Q4130): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2addec
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.m2afdec
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.m1addec
Property / Symbols used
 
Property / Symbols used: repeated integrals of the complementary error function / rank
 
Normal rank
Property / Symbols used: repeated integrals of the complementary error function / qualifier
 
test:

i n ⁢ erfc ⁡ ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}

\repinterfc{\NVar{n}}@{\NVar{z}}
Property / Symbols used: repeated integrals of the complementary error function / qualifier
 
xml-id: C7.S18.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11518 / rank
 
Normal rank
Property / Symbols used: Q11518 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11518 / qualifier
 
xml-id: C12.S1.XMD4.m1cdec

Latest revision as of 14:12, 2 January 2020

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English
DLMF:12.7.E7
No description defined

    Statements

    test
    U ⁡ ( n + 1 2 , z ) = e 1 4 ⁢ z 2 ⁢ 𝐻ℎ n ⁡ ( z ) = π ⁢  2 1 2 ⁢ ( n - 1 ) ⁢ e 1 4 ⁢ z 2 ⁢ i n ⁢ erfc ⁡ ( z / 2 ) , parabolic-U 𝑛 1 2 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Fishers-Hh 𝑛 𝑧 𝜋 superscript  2 1 2 𝑛 1 superscript 𝑒 1 4 superscript 𝑧 2 repeated-integral-complementary-error-function 𝑛 𝑧 2 {\displaystyle{\displaystyle U\left(n+\tfrac{1}{2},z\right)=e^{\frac{1}{4}z^{2% }}\mathit{Hh}_{n}\left(z\right)=\sqrt{\pi}\,2^{\frac{1}{2}(n-1)}e^{\frac{1}{4}% z^{2}}\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z/\sqrt{2}\right),}}
    0 references
    DLMF id
    DLMF:12.7.E7
    0 references
    constraint
    n = - 1 , 0 , 1 , … 𝑛 1 0 1 … {\displaystyle{\displaystyle n=-1,0,1,\dots}}
    0 references
    Symbols used
    probability function
    test
    𝐻ℎ n ⁡ ( z ) Fishers-Hh 𝑛 𝑧 {\displaystyle{\displaystyle\mathit{Hh}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C7.S18.E12.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    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.m1addec
    0 references
    repeated integrals of the complementary error function
    test
    i n ⁢ erfc ⁡ ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}
    xml-id
    C7.S18.E2.m2adec
    0 references
    Q11513
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1fdec
    0 references
    Q11518
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C12.S1.XMD4.m1cdec
    0 references
     
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