Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8917)

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`=5/2

http://functions.wolfram.com/07.22.03.8917.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(13/4)}, -z] == (1/(63778314600 z^(3/2))) (2 Sqrt[z] (-13749310575 + 1978376400 z - 247484160 z^2 + 50319360 z^3 - 26148864 z^4 + 147849216 z^5 + 4194304 z^6) Cos[2 Sqrt[z]] + 1048576 Sqrt[Pi] z^(23/4) (567 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (13749310575 + 11578366800 z - 1349187840 z^2 + 205148160 z^3 - 61931520 z^4 + 72351744 z^5 + 2097152 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]