hypergeometric function (Q3122): Difference between revisions

@@ Property / named after @@
+Carl Friedrich Gauss
@@ Property / named after: Carl Friedrich Gauss / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\mathrm {F} (a,b,c;z)=\sum _{n=0}^{\infty }{\frac {(a)_{n}(b)_{n}}{(c)_{n}}}{\frac {z^{n}}{n!}},-c\notin {\boldsymbol {\mathsf {N}}}$ 
\mathrm{F}(a, b, c; z) = \sum_{n = 0}^{\infty} \frac{(a)_n (b)_n}{(c)_n} \frac{z^n}{n!}, -c \notin \boldsymbol{\mathsf{N}}
+Normal rank
+stated in: ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
section, verse, paragraph, or clause: 2-20.13
@@ Property / defining formula @@
+ $\mathrm {F} (a,b,c;z)={}_{2}\mathrm {F} _{1}(a,b;c;z)$ 
\mathrm{F}(a, b, c; z) = {}_2\mathrm{F}_1(a, b; c; z)
+Normal rank
@@ Property / JSTOR topic ID @@
+hypergeometric-functions
@@ Property / JSTOR topic ID: hypergeometric-functions / rank @@
+Normal rank
@@ Property / different from @@
+hypergeometric series
@@ Property / different from: hypergeometric series / rank @@
+Normal rank
@@ Property / different from: hypergeometric series / reference @@
+inferred from: hypergeometric series
@@ Property / Encyclopædia Britannica Online ID @@
+topic/hypergeometric-function
+Normal rank
+subject named as: hypergeometric function
@@ Property / Microsoft Academic ID @@
+197320386
@@ Property / Microsoft Academic ID: 197320386 / rank @@
+Normal rank
@@ Property / described by source @@
+Great Soviet Encyclopedia (1926–1947)
@@ Property / described by source: Great Soviet Encyclopedia (1926–1947) / rank @@
+Normal rank
@@ Property / described by source @@
+ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
+Normal rank
+section, verse, paragraph, or clause: 2-20.13
+subject named as: hypergeometric function
@@ Property / Freebase ID @@
+/m/06hygx
@@ Property / Freebase ID: /m/06hygx / rank @@
+Normal rank
@@ Property / in defining formula @@
+ $\mathrm {F} (a,b,c;z)$ 
\mathrm{F}(a, b, c; z)
@@ Property / in defining formula: $\mathrm {F} (a,b,c;z)$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathrm {F} (a,b,c;z)$ / qualifier @@
+symbol represents: hypergeometric function
@@ Property / in defining formula @@
+ $(a)_{k}$ 
(a)_k
@@ Property / in defining formula: $(a)_{k}$ / rank @@
+Normal rank
@@ Property / in defining formula: $(a)_{k}$ / qualifier @@
+symbol represents: Pochhammer symbol
@@ Property / in defining formula @@
+ $n!$ 
n!
@@ Property / in defining formula: $n!$ / rank @@
+Normal rank
@@ Property / in defining formula: $n!$ / qualifier @@
+symbol represents: factorial
@@ Property / in defining formula @@
+ ${}_{p}\mathrm {F} _{q}\left(a_{1},a_{2},\ldots ,a_{p};b_{1},b_{2},\ldots ,b_{q};z\right)$ 
{}_p\mathrm{F}_q\left(a_1, a_2, \ldots, a_p; b_1, b_2, \ldots, b_q; z\right)
+Normal rank
+symbol represents: generalized hypergeometric function
@@ Property / in defining formula @@
+ ${\boldsymbol {\mathsf {N}}}$ 
\boldsymbol{\mathsf{N}}
@@ Property / in defining formula: ${\boldsymbol {\mathsf {N}}}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\boldsymbol {\mathsf {N}}}$ / qualifier @@
+symbol represents: set of non-negative integers
@@ Property / OpenAlex ID @@
+C197320386
@@ Property / OpenAlex ID: C197320386 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C197320386 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / instance of @@
+function
@@ Property / instance of: function / rank @@
+Normal rank
@@ Property / instance of @@
+special function
@@ Property / instance of: special function / rank @@
+Normal rank
@@ Property / instance of @@
+hypergeometric series
@@ Property / instance of: hypergeometric series / rank @@
+Normal rank
@@ Property / instance of @@
+generalized hypergeometric function
@@ Property / instance of: generalized hypergeometric function / rank @@
+Normal rank
@@ Property / NL CR AUT ID @@
+ph161655
@@ Property / NL CR AUT ID: ph161655 / rank @@
+Normal rank
@@ Property / NL CR AUT ID: ph161655 / qualifier @@
+subject named as: hypergeometrické funkce
@@ Property / ScienceDirect topic ID @@
+physics-and-astronomy/hypergeometric-functions
+Normal rank
@@ Property / ScienceDirect topic ID @@
+mathematics/hypergeometric-function
@@ Property / ScienceDirect topic ID: mathematics/hypergeometric-function / rank @@
+Normal rank
@@ Property / Stack Exchange tag @@
+https://mathoverflow.net/tags/hypergeometric-functions
+Normal rank
@@ Property / Stack Exchange tag @@
+https://math.stackexchange.com/tags/hypergeometric-function
+Normal rank
@@ Property / image @@
+Plot of the hypergeometric function 2F1(a,b; c; z) with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
+Normal rank
@@ Property / Encyclopedia of Mathematics article ID @@
+Hypergeometric_function
+Normal rank
@@ Property / MathWorld ID @@
+HypergeometricFunction
@@ Property / MathWorld ID: HypergeometricFunction / rank @@
+Normal rank
@@ Property / ProofWiki ID @@
+Definition:Hypergeometric_Function/Gaussian
@@ Property / ProofWiki ID: Definition:Hypergeometric_Function/Gaussian / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID @@
+987007553157805171
@@ Property / National Library of Israel J9U ID: 987007553157805171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007553157805171 / reference @@
+stated in: National Library of Israel Names and Subjects Authority File