DLMF:12.9.E4 (Q4153): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

- 1 4 π + δ ± ph z 3 4 π - δ 1 4 𝜋 𝛿 plus-or-minus phase 𝑧 3 4 𝜋 𝛿 {\displaystyle{\displaystyle-\tfrac{1}{4}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{4}\pi-\delta}}

-\tfrac{1}{4}\pi+\delta\leq\pm\phase@@{z}\leq\tfrac{3}{4}\pi-\delta
Property / constraint: - 1 4 π + δ ± ph z 3 4 π - δ 1 4 𝜋 𝛿 plus-or-minus phase 𝑧 3 4 𝜋 𝛿 {\displaystyle{\displaystyle-\tfrac{1}{4}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{4}\pi-\delta}} / rank
 
Normal rank

Revision as of 17:44, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:12.9.E4
No description defined

    Statements

    V ( a , z ) 2 π e 1 4 z 2 z a - 1 2 s = 0 ( 1 2 - a ) 2 s s ! ( 2 z 2 ) s ± i Γ ( 1 2 - a ) e - 1 4 z 2 z - a - 1 2 s = 0 ( - 1 ) s ( 1 2 + a ) 2 s s ! ( 2 z 2 ) s , asymptotic-expansion parabolic-V 𝑎 𝑧 plus-or-minus 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 superscript 𝑧 𝑎 1 2 superscript subscript 𝑠 0 Pochhammer 1 2 𝑎 2 𝑠 𝑠 superscript 2 superscript 𝑧 2 𝑠 𝑖 Euler-Gamma 1 2 𝑎 superscript 𝑒 1 4 superscript 𝑧 2 superscript 𝑧 𝑎 1 2 superscript subscript 𝑠 0 superscript 1 𝑠 Pochhammer 1 2 𝑎 2 𝑠 𝑠 superscript 2 superscript 𝑧 2 𝑠 {\displaystyle{\displaystyle V\left(a,z\right)\sim\sqrt{\frac{2}{\pi}}e^{\frac% {1}{4}z^{2}}z^{a-\frac{1}{2}}\sum_{s=0}^{\infty}\frac{{\left(\tfrac{1}{2}-a% \right)_{2s}}}{s!(2z^{2})^{s}}\pm\frac{i}{\Gamma\left(\tfrac{1}{2}-a\right)}e^% {-\frac{1}{4}z^{2}}z^{-a-\frac{1}{2}}\sum_{s=0}^{\infty}(-1)^{s}\frac{{\left(% \tfrac{1}{2}+a\right)_{2s}}}{s!(2z^{2})^{s}},}}
    0 references
    DLMF:12.9.E4
    0 references
    - 1 4 π + δ ± ph z 3 4 π - δ 1 4 𝜋 𝛿 plus-or-minus phase 𝑧 3 4 𝜋 𝛿 {\displaystyle{\displaystyle-\tfrac{1}{4}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{4}\pi-\delta}}
    0 references