Everything about Confluent hypergeometric function
Solution of a confluent hypergeometric equation
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. The term confluent refers to the merging of singular points of families of differential equations; confluere is Latin for "to flow together". There are several common standard forms of confluent hypergeometric functions:Kummer's (confluent hypergeometric) function M(a, b, z), introduced by Kummer (1837), is a solution to Kummer's differential equation. This is also known as the confluent hypergeometric function of the first kind. There is a different and unrelated Kummer's function bearing the same name. Tricomi's (confluent hypergeometric) function U(a, b, z) introduced by Francesco Tricomi (1947), sometimes denoted by Ψ(a; b; z), is another solution to Kummer's equation. This is also known as the confluent hypergeometric function of the second kind. Whittaker functions (for Edmund Taylor Whittaker) are solutions to Whittaker's equation. Coulomb wave functions are solutions to the Coulomb wave equation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Confluent hypergeometric functionA 5-minute orientation
- Skim a recent paper: A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functionsInfluential work since 2022
- Pick up a classic book: The confluent hypergeometric functionThe most-reprinted book on the subject
- Read the landmark paper: Extended hypergeometric and confluent hypergeometric functionsCited 107 times
- Go sideways: Hypergeometric functionA closely related topic
- Go sideways: Parabolic cylinder functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Extended hypergeometric and confluent hypergeometric functions
Computing the confluent hypergeometric function, M ( a,b,x )
Operational Representations of Whittaker's Confluent Hypergeometric Function and Weber's Parabolic Cylinder Function
Confluent Hypergeometric Functions
GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
Properties of the Confluent Hypergeometric Function
Study on new integral operators defined using confluent hypergeometric function
The generalized confluent hypergeometric function
🆕 Influential since 2022
A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions
Certain implementations in fractional calculus operators involving Mittag-Leffler-confluent hypergeometric functions
On the analytic extension of three ratios of Horn's confluent hypergeometric function $\mathrm{H}_7$
Fractional Integral of the Confluent Hypergeometric Function Related to Fuzzy Differential Subordination Theory
Beyond Matérn: On A Class of Interpretable Confluent Hypergeometric Covariance Functions
📚 Books worth reading
The confluent hypergeometric functionHerbert Buchholz · 1969
Tables of Airy functions and special confluent hypergeometric functions for asymptotic solutions of differential equations of the second orderA. D. Smirnov · 1960- 📕Collected PapersGoro Shimura · 2002
- 📕Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical TablesMilton Abramowitz · 1972
Confluent hypergeometric functionsLucy Joan Slater · 1960- 📕Tables of Airy functions and special confluent hypergeometric functionsA. D. Smirnov · 1960
- 📕Asymptotic forms of Whittaker's confluent hypergeometric functionsArthur Erdélyi · 1957
- 📕Asymptotic forms of Whittaker's confluent hypergeometric functionsArthur Erde lyi · 1957
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