DLMF:7.9.E2 (Q2396)

From DRMF
Revision as of 01:47, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:7.9.E2
No description defined

    Statements

    Defining formula
    π ⁢ e z 2 ⁢ erfc ⁡ z = 2 ⁢ z 2 ⁢ z 2 + 1 - 1 ⋅ 2 2 ⁢ z 2 + 5 - 3 ⋅ 4 2 ⁢ z 2 + 9 - ⋯ , 𝜋 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑧 continued-fraction 2 𝑧 2 superscript 𝑧 2 1 continued-fraction ⋅ 1 2 2 superscript 𝑧 2 5 continued-fraction ⋅ 3 4 2 superscript 𝑧 2 9 ⋯ {\displaystyle{\displaystyle\sqrt{\pi}e^{z^{2}}\operatorname{erfc}z=\cfrac{2z}% {2z^{2}+1-\cfrac{1\cdot 2}{2z^{2}+5-\cfrac{3\cdot 4}{2z^{2}+9-\cdots}}},}}
    0 references
    DLMF id
    DLMF:7.9.E2
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2396&oldid=34653"