DLMF:33.19.E3 (Q9661): Difference between revisions

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Revision as of 14:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q12666
		Property / Symbols used: Q12666 / rank
			Normal rank
		Property / Symbols used: Q12666 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ell}}$ \ell
		Property / Symbols used: Q12666 / qualifier
			xml-id: C33.S1.XMD2.m1bdec
		Property / Symbols used
			Q12692
		Property / Symbols used: Q12692 / rank
			Normal rank
		Property / Symbols used: Q12692 / qualifier
			Defining formula: ${\displaystyle{\displaystyle r}}$ r
		Property / Symbols used: Q12692 / qualifier
			xml-id: C33.S1.XMD3.m1adec
		Property / Symbols used
			Q12693
		Property / Symbols used: Q12693 / rank
			Normal rank
		Property / Symbols used: Q12693 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\epsilon}}$ \epsilon
		Property / Symbols used: Q12693 / qualifier
			xml-id: C33.S1.XMD6.m1bdec
		Property / Symbols used
			quantity (locally)
		Property / Symbols used: quantity (locally) / rank
			Normal rank
		Property / Symbols used: quantity (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\kappa}}$ \kappa
		Property / Symbols used: quantity (locally) / qualifier
			xml-id: C33.S14.XMD1.m1dec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle A(\epsilon,\ell)}}$ A(\epsilon,\ell)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C33.S14.XMD4.m1dec
		Property / Symbols used
			Q12697
		Property / Symbols used: Q12697 / rank
			Normal rank
		Property / Symbols used: Q12697 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\gamma_{k}}}$ \gamma_{k}
		Property / Symbols used: Q12697 / qualifier
			xml-id: C33.S19.XMD2.m1dec
		Property / Symbols used
			Q12698
		Property / Symbols used: Q12698 / rank
			Normal rank
		Property / Symbols used: Q12698 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta_{k}}}$ \delta_{k}
		Property / Symbols used: Q12698 / qualifier
			xml-id: C33.S19.XMD3.m1dec

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Latest revision as of 14:37, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:33.19.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle 2\pi h\left(\epsilon,\ell;r\right)={\sum_{k=0}^{2\ell}\frac{(2\ell-k)!\gamma_{k}}{k!}(2r)^{k-\ell}-\sum_{k=0}^{\infty}\delta_{k}r^{k+\ell+1}}-A(\epsilon,\ell)\left(2\ln|2r/\kappa|+\Re\psi\left(\ell+1+\kappa\right)+\Re\psi\left(-\ell+\kappa\right)\right){f\left(\epsilon,\ell;r\right),}}}$

0 references

DLMF id

DLMF:33.19.E3

0 references

constraint

${\displaystyle{\displaystyle r\neq 0}}$

0 references

Symbols used

regular Coulomb function

Defining formula

${\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)}}$

xml-id

C33.S14.E4.m2aadec

0 references

irregular Coulomb function

Defining formula

${\displaystyle{\displaystyle h\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)}}$

xml-id

C33.S14.E7.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2adec

0 references

psi (or digamma) function

Defining formula

${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$

xml-id

C5.S2.E2.m2adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5aadec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2adec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1adec

0 references

Q12669

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C33.S1.XMD1.m1bdec

0 references

Q12666

Defining formula

${\displaystyle{\displaystyle\ell}}$

xml-id

C33.S1.XMD2.m1bdec

0 references

Q12692

Defining formula

${\displaystyle{\displaystyle r}}$

xml-id

C33.S1.XMD3.m1adec

0 references

Q12693

Defining formula

${\displaystyle{\displaystyle\epsilon}}$

xml-id

C33.S1.XMD6.m1bdec

0 references

quantity (locally)

Defining formula

${\displaystyle{\displaystyle\kappa}}$

xml-id

C33.S14.XMD1.m1dec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle A(\epsilon,\ell)}}$

xml-id

C33.S14.XMD4.m1dec

0 references

Q12697

Defining formula

${\displaystyle{\displaystyle\gamma_{k}}}$

xml-id

C33.S19.XMD2.m1dec

0 references

Q12698

Defining formula

${\displaystyle{\displaystyle\delta_{k}}}$

xml-id

C33.S19.XMD3.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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