Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.age3)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.age3.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(21/4)}, -z] == (1/12993098493375) ((12993098493375 - 29148538419000 z + 15704254566000 z^2 - 4926311913600 z^3 + 1446052608000 z^4 - 996663951360 z^5 - 2578584698880 z^6 + 99950264320 z^7 - 134217728 z^8) Cos[2 Sqrt[z]] + 2 Sqrt[z] (12993098493375 - 11824407094500 z + 4558146793200 z^2 - 1293104736000 z^3 + 444939264000 z^4 - 1348681728000 z^5 + 381089218560 z^6 - 3003121664 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]