# orthogonality relation

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##### 1: 27.8 Dirichlet Characters
If $\left(n,k\right)=1$, then the characters satisfy the orthogonality relation
##### 3: 31.9 Orthogonality
For corresponding orthogonality relations for Heun functions (§31.4) and Heun polynomials (§31.5), see Lambe and Ward (1934), Erdélyi (1944), Sleeman (1966a), and Ronveaux (1995, Part A, pp. 59–64). … For bi-orthogonal relations for path-multiplicative solutions see Schmidt (1979, §2.2). …
##### 4: William P. Reinhardt
Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …
##### 5: 18.27 $q$-Hahn Class
Thus in addition to a relation of the form (18.27.2), such systems may also satisfy orthogonality relations with respect to a continuous weight function on some interval. …
###### §18.27(iii) Big $q$-Jacobi Polynomials
The orthogonality relations are given by (18.27.2), with …
##### 6: 18.2 General Orthogonal Polynomials
The orthogonality relations (18.2.1)–(18.2.3) each determine the polynomials $p_{n}(x)$ uniquely up to constant factors, which may be fixed by suitable normalization. …
##### 7: 29.14 Orthogonality
First, the orthogonality relations (29.3.19) apply; see §29.12(i). …
##### 8: 15.9 Relations to Other Functions
###### Krawtchouk
15.9.10 $P^{(\lambda)}_{n}\left(x;\phi\right)=\frac{{\left(2\lambda\right)_{n}}}{n!}e^{% n\mathrm{i}\phi}F\left({-n,\lambda+\mathrm{i}x\atop 2\lambda};1-e^{-2\mathrm{i% }\phi}\right).$