Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7701)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-21/4

http://functions.wolfram.com/07.22.03.7701.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 21/4}, -z] == (1/(330301440 z^(17/4))) (-2 z^(1/4) (1149049526625 - 524748123900 z + 115848532800 z^2 - 15178363200 z^3 + 1762133760 z^4 - 209280000 z^5 + 3637248 z^6 + 262144 z^7) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (1149049526625 - 831161331000 z + 201307906800 z^2 - 27020822400 z^3 + 3134419200 z^4 - 395089920 z^5 + 7864320 z^6 + 524288 z^7) Cos[2 Sqrt[z]] - 15 (76603301775 - 157548491100 z + 60064804800 z^2 - 10369719360 z^3 + 1194082560 z^4 - 157031424 z^5 + 12091392 z^6 + 262144 z^7) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (15 (76603301775 - 157548491100 z + 60064804800 z^2 - 10369719360 z^3 + 1194082560 z^4 - 157031424 z^5 + 12091392 z^6 + 262144 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (1149049526625 - 831161331000 z + 201307906800 z^2 - 27020822400 z^3 + 3134419200 z^4 - 395089920 z^5 + 7864320 z^6 + 524288 z^7) Sin[2 Sqrt[z]]))

Standard Form

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MathML 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]