Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5253)

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=5, b_1`>=-11/2

For fixed z and a₁=5, b₁=-9/2

http://functions.wolfram.com/07.22.03.5253.01

Input Form

HypergeometricPFQ[{5}, {-(9/2), 6}, -z] == (1/(756 z^5)) (-1964187225 + (1964187225 - 3928374450 z + 1309458150 z^2 - 174594420 z^3 + 12471030 z^4 - 553512 z^5 + 15424 z^6 - 128 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (1964187225 - 1309458150 z + 261891630 z^2 - 24942060 z^3 + 1385670 z^4 - 49632 z^5 + 928 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]