Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9651)

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`=11/2

http://functions.wolfram.com/07.22.03.9651.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 1/4}, -z] == (1/(300494937600 z^(9/2))) (2 Sqrt[z] (-206239658625 + 9243234000 z - 7110180000 z^2 - 17696448000 z^3 + 57573457920 z^4 + 26574874560 z^5 + 2095795200 z^6 + 45826048 z^7 + 262144 z^8) Cos[2 Sqrt[z]] + 64 Sqrt[Pi] z^(21/4) (19426262625 + 7104461760 z + 534504960 z^2 + 11517952 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-206239658625 + 284229445500 z + 53895164400 z^2 + 16432416000 z^3 - 56628633600 z^4 + 585158492160 z^5 + 224281597440 z^6 + 17035911168 z^7 + 368181248 z^8 + 2097152 z^9) 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]