DLMF:8.18.E14 (Q2682): Difference between revisions

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Revision as of 14:07, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:07, 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
			Q11362
		Property / Symbols used: Q11362 / rank
			Normal rank
		Property / Symbols used: Q11362 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11362 / qualifier
			xml-id: C8.S17.XMD3.m1idec
		Property / Symbols used
			scaled gamma function (locally)
		Property / Symbols used: scaled gamma function (locally) / rank
			Normal rank
		Property / Symbols used: scaled gamma function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\widetilde{\Gamma}(z)}}$ \widetilde{\Gamma}(z)
		Property / Symbols used: scaled gamma function (locally) / qualifier
			xml-id: C8.S18.XMD5.m1adec
		Property / Symbols used
			Q11374
		Property / Symbols used: Q11374 / rank
			Normal rank
		Property / Symbols used: Q11374 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11374 / qualifier
			xml-id: C8.S18.XMD6.m1dec
		Property / Symbols used
			Q11375
		Property / Symbols used: Q11375 / rank
			Normal rank
		Property / Symbols used: Q11375 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q11375 / qualifier
			xml-id: C8.S18.XMD7.m1dec
		Property / Symbols used
			Q11376
		Property / Symbols used: Q11376 / rank
			Normal rank
		Property / Symbols used: Q11376 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h_{k}(\zeta,\mu)}}$ h_{k}(\zeta,\mu)
		Property / Symbols used: Q11376 / qualifier
			xml-id: C8.S18.XMD8.m1dec

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Latest revision as of 14:07, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.18.E14	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle I_{x}\left(a,b\right)\sim Q\left(b,a\zeta\right)-\frac{(2\pi b)^{-1/2}}{\widetilde{\Gamma}(b)}\left(\frac{x}{x_{0}}\right)^{a}\left(\frac{1-x}{1-x_{0}}\right)^{b}\sum_{k=0}^{\infty}\frac{h_{k}(\zeta,\mu)}{a^{k}},}}$

0 references

DLMF id

DLMF:8.18.E14

0 references

Symbols used

incomplete beta function

Defining formula

${\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}$

xml-id

C8.S17.E2.m2acdec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

Q11326

Defining formula

${\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}$

xml-id

C8.S2.E4.m2aadec

0 references

Q11330

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C8.S1.XMD5.m1edec

0 references

Q11360

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C8.S17.XMD1.m1fdec

0 references

Q11361

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C8.S17.XMD2.m1hdec

0 references

Q11362

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C8.S17.XMD3.m1idec

0 references

scaled gamma function (locally)

Defining formula

${\displaystyle{\displaystyle\widetilde{\Gamma}(z)}}$

xml-id

C8.S18.XMD5.m1adec

0 references

Q11374

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C8.S18.XMD6.m1dec

0 references

Q11375

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C8.S18.XMD7.m1dec

0 references

Q11376

Defining formula

${\displaystyle{\displaystyle h_{k}(\zeta,\mu)}}$

xml-id

C8.S18.XMD8.m1dec

0 references

 

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