Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9547)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9547.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(7/4)}, -z] == (1/(6783285600 z^(5/2))) (2 Sqrt[z] (-1964187225 - 924323400 z + 323205120 z^2 - 140359680 z^3 + 195624960 z^4 + 17809408 z^5 + 262144 z^6) Cos[2 Sqrt[z]] + 16384 Sqrt[Pi] z^(21/4) (206625 + 17632 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-1964187225 + 1694592900 z - 1137628800 z^2 + 392555520 z^3 - 263454720 z^4 + 1666449408 z^5 + 144048128 z^6 + 2097152 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]