An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering.
- Provides a historical overview for a family of the special polynomials
- Presents a logical investigation of a family of the hypergeometric series
- Proposes a new family of the hypergeometric supertrigonometric functions
- Presents a new family of the hypergeometric superhyperbolic functions
Arvustused
"Publishers description: The book gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering." --zbMATH Open
| Biography |
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xi | |
| Preface |
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xiii | |
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1 Euler Gamma Function, Pochhammer Symbols And Euler Betafunction |
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1 | (12) |
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1 | (5) |
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6 | (3) |
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9 | (4) |
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2 Hypergeometric, Supertrigonometric, And Superhyperbolic Functions Via Clausen Hypergeometric Series |
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13 | (126) |
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2.1 Clausen hypergeometric series |
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13 | (36) |
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2.2 The hypergeometric supertrigonometric functions via Clausen hypergeometric series |
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49 | (24) |
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2.3 The hypergeometric superhyperbolic functions via Clausen hypergeometric series |
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73 | (24) |
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2.4 The special functions via Clausen hypergeometric series with three numerator parameters and two denominator parameters |
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97 | (18) |
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2.5 Analytic number theory via Clausen hypergeometric functions |
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115 | (24) |
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3 Hypergeometric Supertrigonometric And Superhyperbolic Functions Via Gauss Hypergeometric Series |
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139 | (98) |
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3.1 Gauss hypergeometric series |
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139 | (6) |
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3.2 Hypergeometric supertrigonometric functions via Gauss hypergeometric series |
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145 | (4) |
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3.3 Hypergeometric superhyperbolic functions via Gauss hypergeometric series |
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149 | (5) |
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3.4 Some elementary examples for the Gauss hypergeometric series |
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154 | (15) |
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3.5 Integral representations for the hypergeometric superhyperbolic and hypergeometric superhyperbolic functions |
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169 | (34) |
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3.6 Analytic number theory via Gauss hypergeometric functions |
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203 | (34) |
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4 Hypergeometric Supertrigonometric And Superhyperbolic Functions Via Kummer Confluent Hypergeometric Series |
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237 | (56) |
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4.1 The Kummer confluent hypergeometric series of first type |
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237 | (5) |
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4.2 The hypergeometric supertrigonometric functions via Kummer confluent hypergeometric series of first type |
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242 | (12) |
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4.3 The hypergeometric superhyperbolic functions via Kummer confluent hypergeometric series of first type |
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254 | (11) |
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4.4 The Kummer confluent hypergeometric series of second type |
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265 | (2) |
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4.5 The hypergeometric supertrigonometric functions via Kummer confluent hypergeometric series of second type |
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267 | (9) |
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4.6 The hypergeometric superhyperbolic functions via Kummer confluent hypergeometric series of second type |
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276 | (8) |
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4.7 Analytic number theory via Kummer confluent hypergeometric series |
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284 | (9) |
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5 Hypergeometric Supertrigonometric And Superhyperbolic Functions Via Jacobi Polynomials |
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293 | (52) |
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293 | (16) |
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5.2 Jacobi--Luke polynomials |
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309 | (3) |
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5.3 Jacobi--Luke-type polynomials |
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312 | (33) |
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6 Hypergeometric Supertrigonometric And Superhyperbolic Functions Via Laguerre Polynomials |
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345 | (100) |
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345 | (45) |
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6.2 Extended works containing the Laguerre polynomials |
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390 | (27) |
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6.3 Some results based on the special functions |
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417 | (28) |
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7 Hypergeometric Supertrigonometric And Superhyperbolic Functions Via Legendre Polynomials |
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445 | (26) |
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445 | (11) |
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7.2 Legendre-type polynomials |
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456 | (15) |
| References |
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471 | (10) |
| Index |
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481 | |
Dr. Xiao-Jun Yang is a full professor of China University of Mining and Technology, China. He was awarded the 2019 Obada-Prize, the Young Scientist Prize (Turkey), and Springer's Distinguished Researcher Award. His scientific interests include: Viscoelasticity, Mathematical Physics, Fractional Calculus and Applications, Fractals, Analytic Number Theory, and Special Functions. He has published over 160 journal articles and 4 monographs, 1 edited volume, and 10 chapters. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Methods in the Applied Sciences, Mathematical Modelling and Analysis, Journal of Thermal Stresses, and Thermal Science, and an associate editor of Journal of Thermal Analysis and Calorimetry, Alexandria Engineering Journal, and IEEE Access.
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