DLMF:15.10.E8 (Q5124): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 17:57, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:13, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(10 intermediate revisions by the same user not shown)
		Property / Symbols used
			$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			xml-id: C15.S2.E1.m2acdec
		Property / Symbols used
			Q10759
		Property / Symbols used: Q10759 / rank
			Normal rank
		Property / Symbols used: Q10759 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$ \Pochhammersym{\NVar{a}}{\NVar{n}}
		Property / Symbols used: Q10759 / qualifier
			xml-id: C5.S2.SS3.m1adec
		Property / Symbols used
			psi (or digamma) function
		Property / Symbols used: psi (or digamma) function / rank
			Normal rank
		Property / Symbols used: psi (or digamma) function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$ \digamma@{\NVar{z}}
		Property / Symbols used: psi (or digamma) function / qualifier
			xml-id: C5.S2.E2.m2adec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5adec
		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2adec
		Property / Symbols used
			Q11650
		Property / Symbols used: Q11650 / rank
			Normal rank
		Property / Symbols used: Q11650 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11650 / qualifier
			xml-id: C15.S1.XMD10.m1dec
		Property / Symbols used
			Q11644
		Property / Symbols used: Q11644 / rank
			Normal rank
		Property / Symbols used: Q11644 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11644 / qualifier
			xml-id: C15.S1.XMD3.m1gdec
		Property / Symbols used
			Q11645
		Property / Symbols used: Q11645 / rank
			Normal rank
		Property / Symbols used: Q11645 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11645 / qualifier
			xml-id: C15.S1.XMD4.m1gdec
		Property / Symbols used
			Q11646
		Property / Symbols used: Q11646 / rank
			Normal rank
		Property / Symbols used: Q11646 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11646 / qualifier
			xml-id: C15.S1.XMD5.m1gdec
		Property / Symbols used
			Q11658
		Property / Symbols used: Q11658 / rank
			Normal rank
		Property / Symbols used: Q11658 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11658 / qualifier
			xml-id: C15.S1.XMD7.m1dec
		Property / Symbols used
			Q11651
		Property / Symbols used: Q11651 / rank
			Normal rank
		Property / Symbols used: Q11651 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11651 / qualifier
			xml-id: C15.S1.XMD9.m1dec

---

Latest revision as of 14:13, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.10.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F\left({a,b\atop n};z\right)\ln z-\sum_{k=1}^{n-1}\frac{(n-1)!(k-1)!}{(n-k-1)!{\left(1-a\right)_{k}}{\left(1-b\right)_{k}}}(-z)^{-k}\\ +\sum_{k=0}^{\infty}\frac{{\left(a\right)_{k}}{\left(b\right)_{k}}}{{\left(n\right)_{k}}k!}z^{k}\left(\psi\left(a+k\right)+\psi\left(b+k\right)-\psi\left(1+k\right)-\psi\left(n+k\right)\right),}}$

0 references

DLMF id

DLMF:15.10.E8

0 references

constraint

${\displaystyle{\displaystyle a,b\neq n-1,n-2,\dots,0,-1,-2,\dots}}$

0 references

Symbols used

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2acdec

0 references

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1adec

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.m5adec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2adec

0 references

Q11650

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C15.S1.XMD10.m1dec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1gdec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1gdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1gdec

0 references

Q11658

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C15.S1.XMD7.m1dec

0 references

Q11651

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C15.S1.XMD9.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5124&oldid=44815"