초기하급수의 합공식 - 편집 역사

2021년 2월 17일 (수) 13:00에 Pythagoras0님의 편집

2021-02-17T13:00:49Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T13:17:21Z

메타데이터: 새 문단

2020년 12월 28일 (월) 10:58에 Pythagoras0님의 편집

2020-12-28T10:58:26Z

2020년 11월 14일 (토) 02:33에 Pythagoras0님의 편집

2020-11-14T02:33:34Z

Pythagoras0: /* 관련논문 */

2014-12-15T13:01:46Z

Pythagoras0: /* 관련논문 */

2014-10-22T02:32:41Z

Pythagoras0: /* 사전 형태의 자료 */

2014-10-14T08:14:45Z

사전 형태의 자료

2014년 7월 8일 (화) 08:26에 Pythagoras0님의 편집

2014-07-08T08:26:44Z

Pythagoras0: 찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

2013-01-15T03:30:36Z

찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

Pythagoras0: 찾아 바꾸기 – “네이버(.*)]” 문자열을 “” 문자열로

2012-11-02T20:09:46Z

찾아 바꾸기 – “네이버(.*)]” 문자열을 “” 문자열로

@@ 110번째 줄: / 110번째 줄: @@
 * Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q4907583 Q4907583]

← 이전 판		2020년 12월 28일 (월) 13:17 판
109번째 줄:		109번째 줄:
	* Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic <math>_7F_6</math>-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.		* Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic <math>_7F_6</math>-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.
	* Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.		* Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q4907583 Q4907583]

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
-−
 ==Chu-Vandermonde 공식==
@@ 7번째 줄: / 7번째 줄: @@
 <math>\,_2F_1(-n,b;c;1)=\dfrac{(c-b)_{n}}{(c)_{n}}</math>
-아래 가우스 공식에서 <math>a=-n</math>인 경우에 얻어진다
+아래 가우스 공식에서 <math>a=-n</math>인 경우에 얻어진다
-−
-−
 ==가우스 공식==
@@ 20번째 줄: / 20번째 줄: @@
   \frac{\Gamma(\frac{1}{2})\Gamma(\frac{1}{2}+\frac{a}{2}+\frac{b}{2})}{\Gamma(\frac{1}{2}+\frac{a}{2})\Gamma(\frac{1}{2}+\frac{b}{2})}</math>
-−
-−
-== 쿰머 공식==
+== 쿰머 공식==
- <math>\,_2F_1(a,b;1+a-b;-1)=\dfrac{\Gamma(1+a-b)\,\Gamma(1+\frac{1}{2}a)}{\Gamma(1+a)\Gamma(1+\frac{1}{2}a-b)}</math>
+ <math>\,_2F_1(a,b;1+a-b;-1)=\dfrac{\Gamma(1+a-b)\,\Gamma(1+\frac{1}{2}a)}{\Gamma(1+a)\Gamma(1+\frac{1}{2}a-b)}</math>
-−
-−
 ==딕슨 공식==
@@ 38번째 줄: / 38번째 줄: @@
   {\Gamma(1+a)\Gamma(1+a-b-c)\Gamma(1+a/2-b)\Gamma(1+a/2-c)}</math>
-−
-−
-== Bailey 공식==
+== Bailey 공식==
 <math>\;_2F_1 \left(a,1-a;c;\frac{1}{2}\right)=
   \frac{\Gamma(\frac{c}{2})\Gamma(\frac{1}{2}+\frac{c}{2})}{\Gamma(\frac{c}{2}+\frac{a}{2})\Gamma(\frac{1}{2}+\frac{c}{2}-\frac{a}{2})}</math>
-−
-−
-−
 ==Pfaff 공식==
- <math>\,_3F_2(a,b,-n;c,1+a+b-c-n;1)=\dfrac{(c-a)_{n}(c-b)_{n}}{(c)_{n}(c-a-b)_{n}}</math>
+ <math>\,_3F_2(a,b,-n;c,1+a+b-c-n;1)=\dfrac{(c-a)_{n}(c-b)_{n}}{(c)_{n}(c-a-b)_{n}}</math>
-−
-−
 ==Dougall 공식==
@@ 69번째 줄: / 69번째 줄: @@
 http://en.wikipedia.org/wiki/Bilateral_hypergeometric_series#Dougall.27s_bilateral_sum
-−
-−
 ==역사==
-−
 * http://www.google.com/search?hl=en&tbs=tl:1&q=
 * [[수학사 연표]]
-−
 ==메모==
-*  [http://www.mathematik.uni-kassel.de/%7Ekoepf/hyper.html http://www.mathematik.uni-kassel.de/~koepf/hyper.html]
+*  [http://www.mathematik.uni-kassel.de/%7Ekoepf/hyper.html http://www.mathematik.uni-kassel.de/~koepf/hyper.html]
-−
-−
 ==관련된 항목들==
@@ 95번째 줄: / 95번째 줄: @@
-−
-==사전 형태의 자료==
+==사전 형태의 자료==
 * http://ko.wikipedia.org/wiki/

@@ 107번째 줄: / 107번째 줄: @@
 ==관련논문==
 * Dunkl, Charles F., and George Gasper. “The Sums of a Double Hypergeometric Series and of the First m+1 Terms of 3F2(a,b,c;(a+b+1)/2,2c;1) When c = -M Is a Negative Integer.” arXiv:1412.4022 [math], December 12, 2014. http://arxiv.org/abs/1412.4022.
-* Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic $_7F_6$-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.
+* Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic <math>_7F_6</math>-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.
 * Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.

@@ 106번째 줄: / 106번째 줄: @@
 ==관련논문==
 * Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic $_7F_6$-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.
 * Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.

← 이전 판		2014년 10월 22일 (수) 02:32 판
106번째 줄:		106번째 줄:

	==관련논문==		==관련논문==
		+	* Wang, Chenying, and Xiaojing Chen. ‘A New Proof for Gasper’s Nonterminating Cubic $_7F_6$-Series Summation Identity’. arXiv:1410.5636 [math], 21 October 2014. http://arxiv.org/abs/1410.5636.
	* Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.		* Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.

← 이전 판		2014년 10월 14일 (화) 08:14 판
103번째 줄:		103번째 줄:
	* http://en.wikipedia.org/wiki/		* http://en.wikipedia.org/wiki/
	* http://mathworld.wolfram.com/HypergeometricSummation.html		* http://mathworld.wolfram.com/HypergeometricSummation.html
		+
		+
		+	==관련논문==
		+	* Vyas, Yashoverdhan, and Kalpana Fatawat. “Extensions of the Classical Theorems for Very Well-Poised Hypergeometric Functions.” arXiv:1410.3241 [math], October 13, 2014. http://arxiv.org/abs/1410.3241.

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
@@ 91번째 줄: / 79번째 줄: @@
 * http://www.google.com/search?hl=en&tbs=tl:1&q=
 * [[수학사 연표]]
@@ 109번째 줄: / 94번째 줄: @@
 * [[로그 사인 적분 (log sine integrals)]]
@@ 130번째 줄: / 103번째 줄: @@
 * http://en.wikipedia.org/wiki/
 * http://mathworld.wolfram.com/HypergeometricSummation.html

← 이전 판		2012년 11월 2일 (금) 20:09 판
158번째 줄:		158번째 줄:

	==블로그==		==블로그==
−
−	~~네이버 ]~~