DLMF:18.12.E6 (Q5648): Difference between revisions

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Revision as of 15:31, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:31, 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
			Q11475
		Property / Symbols used: Q11475 / rank
			Normal rank
		Property / Symbols used: Q11475 / qualifier
			Defining formula: ${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$ \ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
		Property / Symbols used: Q11475 / qualifier
			xml-id: C18.S3.T1.t1.r3.m2abdec
		Property / Symbols used
			Q11750
		Property / Symbols used: Q11750 / rank
			Normal rank
		Property / Symbols used: Q11750 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11750 / qualifier
			xml-id: C18.S1.XMD2.m1edec
		Property / Symbols used
			Q11726
		Property / Symbols used: Q11726 / rank
			Normal rank
		Property / Symbols used: Q11726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11726 / qualifier
			xml-id: C18.S1.XMD6.m1edec

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Latest revision as of 15:31, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.12.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Gamma\left(\lambda+\tfrac{1}{2}\right)e^{z\cos\theta}(\tfrac{1}{2}z\sin\theta)^{\frac{1}{2}-\lambda}J_{\lambda-\frac{1}{2}}\left(z\sin\theta\right)=\sum_{n=0}^{\infty}\frac{C^{(\lambda)}_{n}\left(\cos\theta\right)}{{\left(2\lambda\right)_{n}}}z^{n},}}$

0 references

DLMF id

DLMF:18.12.E6

0 references

constraint

${\displaystyle{\displaystyle 0\leq\theta\leq\pi}}$

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2aadec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Q10759

Defining formula

${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$

xml-id

C5.S2.SS3.m1abdec

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

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2adec

0 references

Q11475

Defining formula

${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r3.m2abdec

0 references

Q11750

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C18.S1.XMD2.m1edec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1edec

0 references

 

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