Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5529)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, b_1`>=-11/2

For fixed z and a₁=11/2, b₁=-11/2

http://functions.wolfram.com/07.22.03.5529.01

Input Form

HypergeometricPFQ[{11/2}, {-(11/2), -(9/2)}, -z] == (1 - (20 z)/9 + (656 z^2)/567 - (6784 z^3)/19845 + (256 z^4)/2835 - (2048 z^5)/42525 - (8192 z^6)/93555 + (2818048 z^7)/618866325 - (65536 z^8)/9282994875) Cos[2 Sqrt[z]] + (1/3094331625) (2 Sqrt[z] (3094331625 - 2750517000 z + 1012888800 z^2 - 266112000 z^3 + 79833600 z^4 - 81285120 z^5 + 48087040 z^6 - 458752 z^7) Sin[2 Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]