Special Functions of Mathematical Physics

1992 ◽  
pp. 159-181
Author(s):  
Siegmund Brandt ◽  
Hans Dieter Dahmen
Keyword(s):  
Special Functions ◽  
Mathematical Physics

Special Functions of Mathematical Physics

1991 ◽  
pp. 180-203
Author(s):  
Siegmund Brandt ◽  
Hans Dieter Dahmen
Keyword(s):  
Special Functions ◽  
Mathematical Physics

ITERATIVE GEOMETRIC STRUCTURES

2010 ◽  
Vol 07 (07) ◽  
pp. 1103-1114 ◽  
Author(s):  
GABRIEL BERCU ◽  
CLAUDIU CORCODEL ◽  
MIHAI POSTOLACHE
Keyword(s):  
Differential Geometry ◽  
Special Functions ◽  
Riemannian Metrics ◽  
General Setting ◽  
Mathematical Physics ◽  
Geometric Structures ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Metric Connection

In this work, we propose a study of geometric structures (connections, pseudo-Riemannian metrics) adapted to some fundamental problems of Differential Geometry. Then we find geometrical characteristics of some ODE or PDE of Mathematical Physics. While Sec. 1 contains the general setting, Secs. 2–5 contain our results. In Sec. 2, we introduce a Hessian structure having the same connection as the initial metric. In Sec. 3, we initiate a study on iterative 2D Hessian structures. In Sec. 4, we find pairs (metric, connection) generated by special functions. In Sec. 5, we find geometric characteristics of a PDE.

Transition probabilities for some ‘special' diffusions

1987 ◽  
Vol 24 (4) ◽  
pp. 888-898
Author(s):  
Václav E. Beneš ◽  
Ioannis Karatzas
Keyword(s):  
Transition Probabilities ◽  
Special Functions ◽  
Mathematical Physics ◽  
Legendre Functions

We study the transition probabilities of the diffusions dXt = (1 – exp(Xt))dt + dWt and dXt = – tanh Xtdt + dWt, in terms of special functions of mathematical physics (confluent hypergeometric and Legendre functions, respectively).

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