About the Project
NIST

q-hypergeometric function

AdvancedHelp

(0.003 seconds)

1—10 of 23 matching pages

1: 17.1 Special Notation
§17.1 Special Notation
k , j , m , n , r , s nonnegative integers.
The main functions treated in this chapter are the basic hypergeometric (or q -hypergeometric) function ϕ s r ( a 1 , a 2 , , a r ; b 1 , b 2 , , b s ; q , z ) , the bilateral basic hypergeometric (or bilateral q -hypergeometric) function ψ s r ( a 1 , a 2 , , a r ; b 1 , b 2 , , b s ; q , z ) , and the q -analogs of the Appell functions Φ ( 1 ) ( a ; b , b ; c ; q ; x , y ) , Φ ( 2 ) ( a ; b , b ; c , c ; q ; x , y ) , Φ ( 3 ) ( a , a ; b , b ; c ; q ; x , y ) , and Φ ( 4 ) ( a , b ; c , c ; q ; x , y ) . Another function notation used is the ‘‘idem’’ function: …
2: 17.17 Physical Applications
§17.17 Physical Applications
See Kassel (1995). …
3: 17.15 Generalizations
§17.15 Generalizations
4: 17.18 Methods of Computation
§17.18 Methods of Computation
5: 17.16 Mathematical Applications
§17.16 Mathematical Applications
6: 17.5 ϕ 0 0 , ϕ 0 1 , ϕ 1 1 Functions
7: 17 q-Hypergeometric and Related Functions
Chapter 17 q -Hypergeometric and Related Functions
8: 17.4 Basic Hypergeometric Functions
§17.4 Basic Hypergeometric Functions
§17.4(ii) ψ s r Functions
The series (17.4.1) is said to be balanced or Saalschützian when it terminates, r = s , z = q , and … The series (17.4.1) is said to be k-balanced when r = s and … The series (17.4.1) is said to be well-poised when r = s and …
9: 17.12 Bailey Pairs
Bailey Transform
Bailey Pairs
Weak Bailey Lemma
Strong Bailey Lemma
10: 17.8 Special Cases of ψ r r Functions
§17.8 Special Cases of ψ r r Functions
Ramanujan’s ψ 1 1 Summation
Quintuple Product Identity
Bailey’s Bilateral Summations
For similar formulas see Verma and Jain (1983).