Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afx1)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.afx1.01

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(11/4)}, -z] == (1 - (284 z)/121 + (544 z^2)/363 - (82624 z^3)/114345 - (4096 z^4)/114345 + (557056 z^5)/1715175 - (1048576 z^6)/15436575 + (4194304 z^7)/23880381525) Cos[2 Sqrt[z]] + (1/23880381525) (2 Sqrt[z] (23880381525 - 24209312400 z + 11999398320 z^2 - 6629575680 z^3 - 7413719040 z^4 - 3649830912 z^5 + 70254592 z^6) 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]