30 Functions of a complex variable

See MSC 30 on zbMATH Open.

Name	Tag	Kind	MSC
Power series are differentiable inside the radius of convergence	002X7EK91H	statement	30B10, 26A24
Contour integral	00FWNP9TXY	definition	30E20
Zero of a holomorphic function	00GC8ZQP4Q	concept	30C15
Modulus of the conjugate	00KRCVE7CK	statement	30A99
Principal branch	017BPGVEE8	concept	30A99
Residue at a simple pole	01991NCP7H	statement	30E20
Cauchy's integral theorem	01MPZXYVYF	statement	30E20
Arguments add under multiplication	01W6RKJP01	statement	30A99
Holomorphic functions on a disc have primitives	02AC7JR6G6	statement	30E20
Casorati–Weierstrass theorem	02HHNPC8ED	statement	30D30
Power series of sine	02KTRHQMHN	statement	33B10, 30B10
Riemann mapping theorem	02WHMEG5ZR	statement	30C35
Real and imaginary parts	02ZE6JHJ7G	definition	30A99
Residue theorem	032HKYS329	statement	30E20
Formula for the modulus	034FGCEYX4	statement	30A99
Open mapping theorem	03YEM7JEDN	statement	30A99
Entire function	0419794R0T	definition	30D20
Uniform limits of holomorphic functions are holomorphic	0431RN0R1N	statement	30A99
Disc of convergence	045EWAXY9P	definition	30B10
Evaluation of real integrals by residues	0476QH9846	concept	30E20
Maximum modulus principle	048F2P90WR	statement	30C80
Cross-ratio	05MW7MPRBS	definition	30C35
Equality of complex numbers	05V7J4WD1C	statement	30A99
Isolated singularity	05Z3FC0154	concept	30D30
Order of a zero	064N002TX4	definition	30C15
Radius of convergence	0660QX1VPR	definition	30B10
Pole	066E7PJCYE	concept	30D30
Real and imaginary parts	06J8TEPJPY	concept	30A99
Branch cut	06JYC06JHY	definition	30A99
Existence of Laurent expansions on an annulus	06WHRARZKY	statement	30B10
Contour integral	06ZGPYTWK8	concept	30E20
Argument of a complex number	070PFSYJJR	concept	30A99
Order of a pole	073MWACF1K	concept	30D30
Cauchy–Hadamard theorem	07E5MB1CA2	statement	30B10
Holomorphic functions are analytic	0826SGV3R0	statement	30B10
Picard's great theorem	08QA8QTM71	statement	30D35
Power series of cosine	08W5RN375X	statement	33B10, 30B10
Domain in the complex plane	097KNJFJ7V	definition	30A99
Cross-ratio	09ASMRMD67	concept	30C35
Power series of the complex logarithm	09BG0Y7SZD	statement	30B10
Complex differentiability	09E6T7VYAG	concept	30A99
Complex numbers	09FTAET5Z4	object	30A99
Removable singularity	09R8GC85RB	concept	30D30
Annulus	0AJ0YVK743	definition	30A99
Circle integral	0AP750DHVP	concept	30E20
Möbius transformation	0B346DDAM5	definition	30C35
Essential singularity	0B8837S5T3	concept	30D30
Complex conjugate	0BJV24C4SY	definition	30A99
Goursat's theorem	0BRG85WXYC	statement	30E20
Polar form	0BRXFNQ5JV	statement	30A99
Riemann's theorem on removable singularities	0BSQDZWF34	statement	30D30
Power series converge uniformly on smaller discs inside the radius of convergence	0BWXV7GADW	statement	30B10, 40A30
Complex numbers as pairs of reals	0CBAB9QQ9X	concept	30A99
Riemann sphere	0CDMXGPSES	definition	30F10
Zero of a holomorphic function	0CEGEASY49	definition	30C15
Disc of convergence	0CH4VG15RE	concept	30B10
Complex plane	0CTE7A31XQ	concept	30A99
Annulus	0CW52NV5TC	concept	30A99
Complex differentiability	0D1C9Y1EXA	definition	30A99
Rouché's theorem	0D430QR02W	statement	30C15
Power series in the complex plane	0D6KXBHKC0	concept	30B10
Holomorphic function	0DG0Z72CQD	definition	30A99
Cauchy's integral formula	0DG10TVYPN	statement	30E20
Estimation lemma	0DJMGPN8K9	statement	30A10
Interval of convergence	0ED4HWNDGW	concept	30B10
Liouville's theorem	0EHKVRF4J6	statement	30D20
Domain in the complex plane	0EWMDD6C14	concept	30A99
Cauchy's integral formula for derivatives	0F0H5P5DED	statement	30E20
Complex conjugate	0FTH2E9TAS	concept	30A99
Entire function	0G4F0XB9X2	concept	30D20
Laurent series	0GXMPDNYX3	concept	30B10
Binomial series	0HB0XKDXHH	example	30B10
Modulus is multiplicative	0HYNZE940T	statement	30A99
Riemann sphere	0J78KBPFZB	concept	30F10
Ratio formula for the radius of convergence	0JBMYAA9QH	statement	30B10
Residue	0JFGKKWWFK	definition	30E20
Cauchy's estimates	0JJRENWMP6	statement	30A10
Isolated zeros theorem	0K83KEJ43P	statement	30C15
Modulus of a complex number	0KW2X0TFBX	definition	30A99
Radius of convergence of the binomial series	0KX1MXJ5MR	statement	30B10
Analytic continuation	0M3YQJ81NB	concept	30B40
Schwarz lemma	0MB48XDBY3	statement	30C80
Power series	0MZB06ST2B	concept	30B10
Radius of convergence	0N288P2TB5	concept	30B10
Holomorphic function	0NAHXR1FRH	concept	30A99
exp(1/z) has an essential singularity at 0	0NB31CC4SN	example	30D30
Principal part	0NDV5R6Z6X	definition	30B10
Meromorphic function	0NSD1TPHR0	definition	30D30
Removable singularity	0P18JC72RE	definition	30D30
Residue	0PHN07KVQT	concept	30E20
Argument principle	0PN2BXRS8G	statement	30C15
Jordan's lemma	0PNPG2PP9H	statement	30E20
The exponential series has infinite radius of convergence	0PVJRACB9H	statement	30B10, 33B10
Holomorphic functions with nonzero derivative are conformal	0Q7M6K6VD7	statement	30C35
Holomorphic functions are infinitely differentiable	0QEBN8DGVE	statement	30A99
Order of a zero	0QX19C7K1C	concept	30C15
Möbius transformation	0SG74WBFA2	concept	30C35
Principal value of the argument	0SQSQP748R	statement	30A99
Hurwitz's theorem	0SSKBQN58M	statement	30C15
Möbius transformations map circles and lines to circles and lines	0SXDHQM2MH	statement	30C35
Integral of 1/z around the unit circle	0SXZ68HV6F	example	30E20
Power series of arctangent	0T32ME0A6H	statement	30B10, 33B10
Cauchy–Riemann equations	0T71SSYZ39	statement	30A99
Circle integral	0T7ABX4CWE	definition	30E20
Isolated singularity	0TYB3HM9KE	definition	30D30
Principal part	0TZ2DPT0JV	concept	30B10
Power series in the complex plane	0VARVQ9ZW1	definition	30B10
Morera's theorem	0VDD7W0EKZ	statement	30E20
Conformal map	0VHNKP1N3K	definition	30C35
Power series	0VP56B4EMX	definition	30B10
Branch cut	0W8QHVSN95	concept	30A99
Pole	0WPQYW8MTE	definition	30D30
Laurent series	0X3XD2ATB0	definition	30B10
Cayley transform	0X45ZM731G	example	30C20
Identity theorem	0YBVKMYX0W	statement	30C15
Order of a pole	0YK27TJ4WF	definition	30D30
Essential singularity	0YKDJBV26S	definition	30D30
Principal branch	0YKY4M3KRQ	definition	30A99
Power series are holomorphic in the disc of convergence	0YMP521ZR5	statement	30B10
Fundamental theorem of contour integration	0YQ458D7PF	statement	30E20
Conformal map	0YYT36R4YD	concept	30C35
Mercator series	0YZXNE3HFR	statement	30B10, 33B10
Interval of convergence	0Z5R9TVWQH	definition	30B10
The complex conjugate is not holomorphic	0Z8ATBPM5W	counterexample	30A99
A complex number times its conjugate	0ZB7J071WQ	statement	30A99
Meromorphic function	0ZZ7ZYDR8W	concept	30D30
Argument of a complex number	0ZZRSX91QR	definition	30A99