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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), -(21/4)}, -z] == (1/501488012025) (-3 (-167162670675 + 356034779100 z - 157556599200 z^2 + 35178010560 z^3 - 5833175040 z^4 + 1112702976 z^5 - 1695547392 z^6 + 130023424 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (501488012025 - 399453654600 z + 118371773520 z^2 - 21806547840 z^3 + 3576545280 z^4 - 953745408 z^5 - 1355808768 z^6 + 8388608 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]